I'm not 100%, but I feel like the 'Cat Person' series of titles is a requirement for some scenes, for example, that scene where she lays her head on your lap and an option appears that says 'stop her', after my 'Cat Person' evolved a couple of times, a new option appeared called 'Let her continue' or something like that, which is really op by the way, it gets you all the way to 4 hearts basically, that's also the reason I think it's more title than affection related, before evolving the title a couple times, even high affection didn't give me that option.
Also if I remember correctly, the option to ask Lani to enter your party before registering at the guild only appears if you have a certain level of that title, which gives a new scene where you register together.
Btw, you can save before clicking the bed button to sleep and reload, or simply click it, rollback with 'PgUp' or 'Scroll Up' on the mouse and click the bed again, each time you click it's randomazed, so instead of having to go trough an entire new day, you just do 'rollback>click' until the scene you want happens, the minimum requirement for that scene where she lays on your lap appears to be the second heart unlocked, so after that scene where she masturbates in her bed and the second level unlocks it appears.
Edit: just realized, you didn't mention which tent you have, but you mentioned cooking set, which may mean you have the small or medium one. I'm pretty sure the dungeon tent is a hard requirement, it's alluded a few times they would only be comfortable enough to do anything if they had the dungeon tent as it drives monsters away and they don't need to do night watch as they do with other tents.