Lawful Evil is any megacorporation or a landlord that throws out a widow with 5 kids in the winter because she couldnt pay the rent.
If this amounts to, "We follow the rules without mercy.", then yes this is either LE or LN.
But LE is even more likely to have been proactive here and thrown her out when she became a widow because women aren't allowed to live alone but must have the protection of a male relative or husband. If such a protector couldn't be found, they would have likely assumed that the best solution is to enslave the widow and her 5 kids to ensure that they neither created the social ill of starvation or beggars nor created the social ill of indebtedness. And if they could not be enslaved, then death by exposure would have not been something that happened by accident, but an end actively sought after to decrease the surplus undesirable population - shipping these undesirables to a work camp or death camp to prevent them from tainting the valuable portion of the population.
Note that in even the LE and LN case, that there was not some social role that a widow with 5 children was not to be reassigned to after losing their current station would be seen as a societal failing. In a LN society, the landlord isn't wrong (and is indeed right) for throwing out the renters that can't pay rent. The landlord himself after all only has usury of the property that rightfully belongs to someone of higher station, and so would be showing poor stewardship to give the property away when the only reason he has a right to it at all is to use it for the benefit of his liege. But the society would be wrong if there didn't exist some work house, poor house, orphanage or other institution for the destitute to resort to (even a prison or slavery). This institution would and should by no means be a merciful one, merely a means by which the least valuable persons to society could properly retire to so as to avoid burdening the society unduly and perhaps show their worth by eventually returning to a productive caste. Indeed, the LE society would probably make the institutions harsh on purpose, both to discourage anyone from resorting to them and to punish those that did. Indeed, in some since the widow and child would be blamed for her state and would be seen to deserve ill-treatment. But regardless, if these institutions didn't exist, and they wouldn't in a chaotic society, then a lawful evil society or person would be appalled. Conversely, in the CN society, they'd probably be appalled that the widow wasn't legally allowed to prostitute herself to pay her expenses without facing ostricization. Only the CG or NG society would expect the landlord to bear the burden of a rentless tenant out of charity. The LG society would probably devote a certain percentage of its resources toward creating living quarters for charity cases, but would largely expect the widow's relations to bear the burden of her upkeep.
However, it's also possible for a miser to have CE motives regardless of the society around him. That is, he's not concerned about throwing the widow out because he thinks she deserves it, or because society says he should or has the right to. He throws the widow out because it costs him money, which in turn costs him comfort or power. You can think of its as the LE landlord would be appalled that someone would throw a widow and 5 kids out who was paying her rent, simply because someone else offered to pay more for the property because as a rent payer she deserved the property, where as a CE landlord would be appalled that someone wouldn't throw out the widow when a better offer was on the table simply because greed. Whereas conversely, the LE landlord would still throw a widow out who bribed him not to, where as the CE landlord would of course not. But neither would be acting out of kindness in either case, because they are evil. Not that a person of an evil disposition couldn't be kind on rare occasions, but it would be out of character and provoke a sort of moral crisis. That is, they'd feel guilty for being kind, and would tend to upbraid themselves for their weakness.
Indeed, the lawful (evil) society is likely already organized to prevent the situation you describe, with substantial rent controls in place and properties classified according to the caste of person who is allowed to rent them. The lawful situation is more likely to be something like, "Widow Douglas. This property as you know is a class 7 residential dwelling, and as you have no husband you are not entitled to more than a class 8 dwelling. Either you must take a husband before the end of the month, or a new dwelling will be assigned to you. I suggest going to the Ministry of Work immediately, to put your name on a waiting list to receive employment. Also, I suggest you consider selling some of your children, as you won't be able to support them in a class 8 salary even if one is available." That description is anachronistic in most fantasy settings, but while far from the language it is not that far from the reality of feudalism. The question of whether she could pay is irrelevant, since in a strongly lawful society it would be obvious that she couldn't, since any unexpected income that would allow her to pay would have to have come from an illegal source anyway.
In the middle ages most areas were organized along slave/master tenant/lord relationships. Serfs did not own the land they worked, which in theory belonged to the lord. But a higher caste serf couldn't (easily) be dispossessed of the right to use that land, even if they failed to pay their rent. The lord could in effect force the tenants to pay any sort of fine he liked to recover the lost rents, but he couldn't legally throw the serf off their land. And even in cases where the lord had a legal right to dispose of the legal contract with the serf, they'd seldom actually do so because demoting the serf to full slave meant that though you had a right to all their labor, you also had a responsibility to take care of them. If a serf starved, it was their fault. If a slave starved, it was your fault. Also, it tended to make the rest of your serfs more restive.
UPDATE: I realize rereading this, that I should have probably made the CG criticism of the situation where the landlord throws the widow out more clear. The CG person examining the situation would say that the reason the landlord threw the widow out, is that the government gave the landlord no real choice in the matter, since the landlord owed the government taxes on the property that he had to pay regardless of how he used it. As such, the landlord did not really own the property and could not dispose of it how he wanted to - even if he was charitably inclined - because the government only allowed him to keep the property on the stipulation that he makes it profitable to the government. (CG argues that to the extent you should be taxed at all, it's never on the ownership of something, which would make the one collecting the tax the true owner, but solely on the use.) If the landlord had chosen to keep the widow in the property, then he would have done so at the risk of being made destitute (by the government which would insist on collecting taxes on the property even when it provided no income) and exposing himself and his family to the same risks. So of course, under this circumstance, you couldn't expect many people to heroically resist authority by being charitable since true charity is something of an anathema to most lawful societies (that will insist most benevolence has to come from not from individuals, but be handed down from legitimate authority as a benefice, thus solidifying the need for the authority and the reason to propitiate it). And while the CG person would naturally see the LG society as being less depraved than the LE society, it would judge both to have the same basic flaw. Conversely, the LG argument would go that you can't rely on individuals since individuals are inherently selfish and will at best only take care of their own, and too many will fall through the cracks and be abandoned.
