Is L familiar with polyamory and you having an open relationship? Has she given an indication that this is something she may be interested in as well?
If she is monogamous, I would keep your feelings to yourself until her relationship with H has dissolved on its own terms. Making a move on a woman in a monogamous relationship isn't kind to her partner, nor is it kind to put her in a position to have to choose between you. If there are problem in their relationship that they are working on, and then she finds out she could just leave him for you, it might make her less likely to want to work on those problems.
Whatever problems her partner may have, be it depression or whatever psychological things he has going on, if she's still with him now, there's a reason. Just because someone is depressed and moody does not mean they do not deserve to be loved.
Another thing to remember is that friends tend to only vent when they have something to gripe about, and are less likely to call you up and tell you how great things are going when they are, because they're too busy enjoying it, and you don't need "support" for for positive feelings
This can lead outsiders to think that the relationship is nothing but problems, simply because you're not privy to the good stuff.