Hm, do you know when does this option appears for Lois?Assuming you have NTR turned on. If I'm remembering correctly most of her NTR scenes are tied behind marriage and buy/moving to the expensive house in the Hot Spring Town. There's NTR scenes in the onsen [I think you have to fuck/show your mom off first in the Onsen]. There's also a NPC that visits your new home if your are away for to long [If I remember right I think he was a friend of your father or something]. So you'll probably have to NG+ with a good chunk of change and you can speed run to marriage.
I don't remember if Lois (I'm assuming that's the prostitute) has NTR scenes per say but when you marry her she intends to quit protitution and you have tell her to continue it, but I think its just sprite scenes don't recall seeing a unique scene for her. Her and Mom probably have the most marriage exclusive content (Might be the only ones lol).
This is all from the top of my head haven't played this game in quite a while but I might just redownload it again cause I really enjoyed it.
Also, how much time do I have to be away from home for Mirei to do things with the neighbor? I went away like 10 times and did various things and came back and nothing happened