I have a Tiagra rear derailleur. On the last ride I heard an annoying squeak coming from somewhere in the back of the bike. Upon checking it at home I found the lower derailleur cog to be squeaking. I turned the bike on it's side and tried to work some Pedro's wax into the bearing, still squeaks. The question is, can I remove it from the bike and take it apart to lubricate, or just replace. Thanks for reading.
Those jockey pulleys have plain bearings, and once the grease dries out, they'll chirp like robins in the springtime.
You can temporarily quiet them by squirting some lube as close as you can get to the pulleys' centers,
or you can solve the problem for a long time to come by removing the pulleys, cleaning and re-greasing the bearing surfaces, and reassembling them.
One tiny tip: Invert the bike, remove the rear wheel, and before you do anything else, snap a cameraphone photo or three of the RD. That way you won't struggle Rubik's Cube style when you go to reinstall the pulleys and properly route the chain.
Otherwise, this is a dead-simple bit of maintenance.