The phrase "had law on" typically refers to an individual or group's insistence on following a strict code of conduct or adhering to a set of rules. Synonyms for this phrase might include being legalistic, rule-oriented, or strict. Other words that could be used to convey a similar meaning might include disciplined, principled, or scrupulous. Depending on the context in which the phrase is being used, other synonyms might also include following the letter of the law, being conformist, or being sticklers for the rules. Ultimately, the key takeaway is that anyone who "has law on" is likely to be focused on following a set of predetermined rules and guidelines in all aspects of their life.