Lieberthal is a fine offensive catcher, and I'd be inclined to just leave him in the starting role unless he goes into a slump. He will probably hit at least .280 for the season this year, and that's what you should be looking for in a catcher, one that doesn't hurt your batting average and everything else is a bonus. Hernandez has slightly better power, but is probably only a .250-.260 hitter.
I wouldn't bother making a trade. Jorge Posada would give you more power from the catcher position and Pudge Rodriquez would give you some steals, but those slight upgrades aren't worth the premium you'd have to pay to get them. With Piazza down, I don't think there really is any elite catchers right now. Rather than go for a better catcher, try to get power and speed stats from your outfield and utility slots.
I would stick with Lieberthal as well, and drop Hernandez and if you really want to deal someone and get an upgrade, I would try to deal Ichiro and with him try to get Posada, you may have to throw in one of your 2B though, but I think you are fine where you are at. Your OF is stacked though. Look to deal something there to maybe upgrade a different position.