It has been a LONG time since I've pursued or produced legal deposition video, though I still occasionally get calls for putting together "day in the life" videos for the infrequent attorney seeking to reflect how the client is, or is not, getting through life due to some situation and a pending lawsuit.
When I did do them there could be NO editing and the footage had to be day/date stamped, plus a vocal announcement at the beginning regarding time, date, place, case (or whatever) number, parties present, representing whom, and myself as the recording videographer. What followed, in my experience was either feed from a PZM boundary or conference mic, no mixer, feeding directly into my camera's L/R audio inputs.
In my early "tape" days I handed over the tape to the hiring party, and later copies using a three-deck system I brought along, feeding via a DA (distribution amp) directly into each deck. I've never had to mic-and-mix using multiple lavs.
I would suspect that the current demand would be "on-site" direct-to-DVD recorder copies and the master. Someone with more up-to-date experience and knowledge will have to pipe in regarding that.