Lawful Good, and Lawful in general, do not lend themselves to tolerance. Lawful societies would regulate what behaviors are appropriate, with the Good/Evil spectrum determining what is okay. But none of them would allow much leeway for divergence or freedom of expression...which are Chaotic traits.
In the realm of Dungeons and Dragons, Lawful Good is best expressed by the paragons of the ethos: Paladins. Between Detect Evil and Smite Evil, I think their level of tolerance is made very clear...
I address this argument later on in my post, but once again there is a big difference between tolerance of freedom of expression and tolerance of actual evil. If your neighbor paints his house yellow, and you prefer blue and think yellow is ugly, it's quite likely under a lawful moral code that not only is your neighbor allowed to pick yellow but you are required by that same moral code to be tolerant of your neighbors mysterious love of yellow.
Furthermore, even if your neighbor has some sort of vice, like he's a late riser, he never does his yard work, he doesn't paint his house regularly enough, and you know he's a bit on the slothful and lazy side, it's very likely indeed that the Paladin's moral code even though he recognizes this as a vice requires him not to smite his neighbor (in any way, even a harsh word). Very likely there is some expectation of imperfection in the world which has to be creatively and productively addressed (creation and production being very good things) rather than going around destroying everything because it isn't perfect (most especially you neighbor). Furthermore, very likely the code is likely to see annoyance, anger, and derisive thoughts to be themselves just as evil or even more evil than the neighbor's sloth and untidiness. Self-control, patience, and stoicism are very likely to be lawful virtues you are expected to possess. All that smiting ability is intended only to address things that can't be addressed in any other way,
There are a ton of things you can choose that don't rise to the level of moral choice. Chaotic societies are likely to have a general axiom like, "Everything that is not forbidden is permitted." Lawful societies are very likely to have a lengthy list of all the freedoms you are permitted that aren't considered anti-social or evil, and trespassing against your neighbors freedoms in those areas is likely to be considered anti-social or evil. But if either society is actually good, neither society is going to tolerate evil. The difference is likely to come at what level either society decides to punish evil, but both societies as a practical matter will have some level of evil which is disapproved of but which may not be legally punished - things that are considered bad but not bad enough to legally punish much less smite. The two will probably differ over the details, with the lawful society tending to see minor punishments as being a more effective means of encouraging change and positive habits than chaotic ones, but there will be in both some level where they recognize humans are not in fact perfect and that you have to tolerate that. Likewise, they will both recognize the huge potential flaw of thinking you are more perfect than your neighbor.
Mercy is a lawful good trait, and tolerance is ultimately a form of mercy. It annoys how many portrayals of Paladins are lawful evil. If you can't figure it out, ask "What would Steve Rogers do?"
