In both the cases you mentioned, making the salt will generally only make it harder to get the solute out.
If you have lidocaine in water, it's probably already the salt. This page (not sure of its legitimacy, but seems reasonable) says lidocaine is practically insoluble in water. Lidocaine•HCl, however, is very soluble in water. In that case, deprotonating (with sodium bicarb, for instance) and filtering the lidocaine would remove the water. You could then reprotonate with anhydrous HCl (in ether would probably work best, if you've got it) and filter or something along those lines, if you need the salt. It is already a solid, though, so if you don't need the salt, the last step is unnecessary.
With caffeine, if the free base, you could extract with DCM a few times and recover most of it. Again, reprotonate with some form of anhydrous HCl. If it is not the free base, same process as the lidocaine, except extract instead of filter, so add base to deprotonate, extract with DCM, remove DCM through evaporation/distillation, and reprotonate if you need the salt.
The one instance where I would say the aqueous salts would be better is if you were going to remove the water by evaporation. Rotovapping or lyophyizing from water should allow you to recover the HCl salts.
If you're doing this in your home or somewhere without sophisticated labware, it will likely be a challenge to get the caffeine. The lidocaine base would be fairly simple. Reprotonating without redissolving would be hard because I'm assuming you don't have any HCl in ether laying around.