I don't think you understand.
Lawful types are the ones who make and uphold the rules that make it so a poor man stealing to live ought to be punished, and the rules that likely made him poor in the first place.
There is a reason 'to be lawful or good' is a question constantly posed in pieces about the paladin: they're not a harmonious pairing.
Or you can approach in the much more rational way, which looks at those "to be lawful or to be good" questions as exactly what they are, ridiculous sophistry.
Law is, by definition, teleological. It serves a purpose, achieves some
end. Hence, law cannot tell us
what that purpose should be. A lawful neutral person does not particularly care what a law is drafted to do, simply that it does in fact do whatever that is; an LN person is perfectly capable of opposing law, not because it is benevolent or malevolent, but because it is
malformed.
A Lawful Good person is, thus, someone who says that the one (and only) valid purpose laws may serve is the good. Obviously, that means they need to develop a refined sense of both whether laws are effective, and what "the good" actually
is so they can know whether laws pursue it. Given laws are necessarily weakened by being constantly replaced or modified, it is efficacious for the LG person to desire to work within the system,
when that is still compatible with doing good. If a law is clearly in violation of the good, then--to the LG person--that is
necessarily a bad law, and the only appropriate lawful response to bad law is to attempt to fix it (if it is worthy and simply ineffective/counterproductive), replace it (if its goal is worthy but its design is simply impossible to achieve as-is), or repeal it (if its goal is inherently unworthy.)
There is no conflict here. Law is, by its own definition, a set of tools. Any such tool that fails to do what it was made for is a tool that must be repaired, replaced, or discarded--but one does not repair, replace, or discard tools willy-nilly, because that's foolish.