Yeah, that is tough. However, I think that long term, the best way to deal with it is with everything out in the open. Maybe talk about polyamory around L and H and see what they think. I generally try to act by putting myself in everyone's place. Since H has a big chance to be hurt by this, I think nothing should happen behind his back.
But for full disclosure, I do know some couples who prefer the affair model of nonmonogamy. They don't like polyamory, but they are ok with their partner being with someone as long as it doesn't complicate their life and they never have to heard of it.