it's more that if she gets married as a noble, she'll have to do things to keep up appearances, so she'll have less time for painting, as well as that fact that if she were to sell her paintings on the market, she'd have to a) keep her identity hidden as a women, because then it would discredit her and b) she wouldn't be able to keep her own funds, since by marrying, the ruler of the household (her husband) would be in control of the household income and so she herself wouldn't exactly be earning it for herself, it'd go to the household finances if that makes sense? and then purchasing supplies would be a conflict of interest, where they'd have to falsify the reason the supplies were purchased, since noble-born ladies were expected to host tea parties and embroider, not paint
tldr she wants to stay single to have the freedom of time and finance to pursue her own interests
She never really told him to stay with her, actually, she said since the beggining she didn't want him to pursue her since she wanted to persue her own goals. Him telling her he'd buy her paintings it's like he is belittling her dreams to become a painter, having people recognizing her works and wanting her works, due to his own selfish reasons. She doesn't want the money, she wants the recgonition, she wants people from different homes admiring her paitings and wishing to have her work on their walls. I get that they have to find the best solution if both of them care for each other and want to be together, but, in the end, what he suggested will probably not be the right one. Not for Lily, at least.
It was explained in previous chapters, but in this world women have two problems:
one) they can't make their own money, can't have their own business, can't use their own talents for their own gain (hence why Lily's mom said she found poor noblewomans to make that embroiement (? forgot how to right this in english sorry its not my first language) for her and, since she can't pay them, she'll give them gifts like rice and food. also, in previous chapters, i remember her talking to the queen about it as well)
two) they can't be painters. i don't recall what was the explanation, but once Mil's and the Baron discovered that Kyle (i think thats the name), the famous painter, could have been a woman, they talked about it (also when they realized Lily also was very interest in it). In this world, painters can only be men and they even worried about what would happen if people found Kyle's real identity (even saying that her paintings would drop value)
Well the thing that the male leads in this story are like walking on eggshells every time they speak with female leads make everything uncomfortable sometimes. Maybe it is better to end up like her sister, who is not apparently interested with anybody.
I understand the recognition part and what she tries to do, and I like this character, but as I have said, making a man next to her try to do something to make her love him that she will only step on it and move on... It is sad, that is just my opinion xD

Oh boy, i understand you are so in love with Lily, but that's not the right answer to the issue. She'll not be happy, probaly offended.