SRD said:
Lawful characters tell the truth, keep their word, respect authority, honor tradition, and judge those who fall short of their
duties.
Lawful Good doesn't have to align with our current views on either "Lawful" or "Good". Aligning with the accepted rules of society, the traditional values if you will, is what matters, and that is specific to the society they live in.
More than a few societies have considered intercourse as a perfectly natural thing, and relatively casual. Marriage was for raising a family, but wasn't required for simple fun.
Japanese, for example, used to consider a little roll in the hay as a way to clear the mind and relieve tensions on the night before a battle. And trust me, nobody was more "lawful" than the Samurai warriors of the Shogun era.
Many a noble had a number of concubines, and a Harem was almost required, socially, if you were a successful man of means in the mid-east. And how many wives did King Solomon have?
During the Renaissance, the Roman Catholic Church owned a number of brothels in England, for while they officially disapproved of pre-marital sex, they also believed that if a man didn't release regularly he would suffer health problems.
In the Roman Empire, the temples of the fertility goddesses functionally *were* brothels.
So, as long as your Monk was willing to take responsibility for any, ahem, results of his pleasures, there's nothing inherently unlawful in enjoying a night well spent.
Now, here's the bad news. The DM decides what the accepted standards and traditions of society are, so if he says that tavern girls are off limits for lawful characters...