If anything, the text suggests that it is Lena who insists on splitting everything in half more than Harold, even though this means she often has to pay more because she only has a salad for the lunches that they have together, whereas it is implied that Harold eats a great deal more. Note what Lena herself says about this splitting of the bill:
And we just continued that way, everything right down the middle. if anything, I encouraged it. Sometimes I insisted on paying for the whole thing: meal, drinks and tip. And it really didn't bother me.
This splitting of the bill therefore seems to reveal more about Lena's character than it does about Harold's character, as in this ability to split the bill Lena expresses her fierce determination to be independent and not to be owned or viewed as a possession that can be bought by any man. The way that she confesses it never "bothered" her to have to split the bill or to pay it herself indicates that she is not a woman who expects a man to provide for her, and that she is happy to pay her own way.