To be honest, I'm pretty sure she has enough money to live a decent life without ever having to work, but she might not have enough money to pay for
that house, assuming the owner even wants to sell it. Korean traditional houses, I assume, must be worth more than the nominal value of the real estate, and there might be personal attachments to them on the part of their owners.
My guess is that Lisa might be so attached to her house (a part of her mother's curse on her) that she will go back to acting (based on the title of this chapter) not necessarily because she needs the money, but because she wants to remain in the place.
It may also be that she doesn't know how to take care of herself given the cossetted life she's lived so far.
As for Oh Dowon…
@saenahonce, I get where you're coming from, and it's fine if they don't end together, but if they do, I see it less as his saving her, and more as their saving each other. It's not as if Dowon doesn't need saving. In fact, he may be in a worse situation than she, though my guess is that at first, it will look like he's saving her.