au> The lock is not to be filled completely, rather only the "pool" at the bottom opening. The volume of air displaced can be pumped into a tank right outside the hull wall, under the fairing. In order to open the outer lock, the pressure must be equalised. So the air can take the same volume in the outer tank across the hull wall, and no more water can enter then the air is pumped into the tank. Actually, no pumping would be needed at all, as the water comes from the bottom side and compensating tank can only be above the water level. Low-pressure pumping would be needed only to remove the water, essentally moving it a meter or so below the "pool" water level. The volume of water in the "pool" can also be minimal — there is no reason for taking water in. Essentially, the perfectly controlled lock operation would not affect the trim. So a small tank would accomodate any imperfection in process control. So... And the mass of the ROV ?
To oparate with your ROV, you're need avery low speed and maybe 0 speed... Your sub needs a dynamic control for the stability...