There's minimal places, period. Let alone for LA's.
Across from the DC channel marina's is National Airport. South of that is a sailboat marina run by the US Park Service (which as gov't policy doesn't allow live-aboards) and has gated parking. Next is "Old Town" Alexandria which has a sea wall for temporary tie-ups and a small, private boat club. Further down river just outside the city is Belle Haven, another US Park Svc marina and which is very, very shallow.
Then several miles down river, past Mt. Vernon, is the next one, Mt Vernon Yacht Club. It's a boating country club sort of place, deep in the middle of an upscale suburban neighborhood. Then several miles down to Woodbridge and Occoquon where there are some small marina's which are full of non liveaboard boats. From visiting there I doubt they'd allow or have facilities for LA's.
From there it is waaaaaay down river to south of the Rt 301 bridge before you get another real marina around Colonial Beach. That's commuting to Richmond territory, not DC.