I don't know that there's anything you can do unless L decides to discuss the issues. It takes the two of you to negotiate issues, not just one of you. Without him taking an active role in negotiating things...well, there's no negotiating things.
He just may not be able to deal with a poly relationship, even if he's just poly to the extent that he's in a mono pairing with a poly partner. There are no magic words to engage somebody who's just not interested in discussing an issue. It may end up that you have to decide on one or the other.
When speaking of various forms of non-monogamy...it ain't poly if you're just fucking around.
While polyamory, open relationships, and swinging are all distinctly different approaches to non-monogamy, they are not mutually exlusive. Folks can, and some do, engage in more than one of them at a time--and it's all good.