I would propose structuring the buyout in the form of convertible debt instead of a cash buyout. You give up your equity today, but the LLC gives your a convertible note to cover your valuation conditional on some future funding event. Set a specific valuation target, at which point the note will pay in cash equivalent to a certain percent of the company's equity. That defers the issue of liquidity until if/when the…
This makes a lot of sense. An issue I have with this is that one reason my co-founder wants to split is that they don't really want the pressure of running a startup, and so are unlikely to go on to raise additional money. Could a situation where I get a cash payout, say $20k from the company to sell a certain %, and then the convertible debt to sell more in the future work?
Whereas it sounds like you have a solid plan to grow the business and generate revenue. As @jedberg says, this makes your interests aligned with the (neutral) investor, and the other founder at odds with the investor.
a) You and your cofounder can't work together
b) One must leave
The investor and one founder can push out the other founder. Who do you think the investor thinks should leave if you reread your quote above?