I realize that this is a two year old thread, but just in case anyone else is looking for a solution to the same problem...
There are many cases online wherein just what you've describe has happened to other LXD55/75 owners - the R.A. motor can be heard running, but there's no motion. And as far as I've seen, it has always been a loose set screw on one of the drive-train spur gears (two of mine were loose last time I checked). You can quickly check this by popping-off the little black plastic inspection covers from either the R.A or the Dec. units, without needing to remove anything more from the mount. After the cover is taken off, you'll see the two spur gears that are the likely culprits. There is most definitely a set screw that's supposed to bear down on the flat of the shaft, holding these gears in place. It's teeny, and it's even possible that it has fallen out completely - can't tell w/o looking. But you can't tighten a loose set screw without removal of the black plastic drive modules. No worries - separation of either of these units from the mount requires the removal of just one screw. You can do it.
This is for my LXD75, but I don't think there's any difference in this particular aspect.
To remove the RA motor & worm assembly, you need to remove just one screw. For this you'll need a 3/16"*** hex key/allen wrench.
[ *** CORRECTION: 3/16" will work, but you should really use a 4mm hex key. I just bought a set of 10 metric hex keys at Home Depot for $5 usd, w/ a lifetime gaurantee! ]
But before you do anything: REMOVE OTA AND COUNTERWEIGHTS FROM MOUNT! We don't want no stinkin' surprises.
O.K. Now we can begin.
Now, fInd the little hole that runs parallel-to and just below the polar-alignment scope. In other words, if you're looking through the polar alignment scope, keep you head and eyeball in the same postion and lower your head approximately 1 1/2". Now you're looking into the little hole we seek.
Insert your allen wrench into this little hole and seat into the screw head. Turn it counter clockwise, while holding the black plastic motor unit with your other hand to prevent it falling onto the floor and making you say a bad, bad word. Because this one screw is the only thing holding it to the mount head. Once it's off you can easily access the two spur gears - they'll be either, aluminum, brass, or one of each (like mine). Meade used different combos during different runs of '55's and '75's over the years. Tighten any loose set screws you find. That's it. Put it back together.
I hope I've gotten this right and also made it clear. If not, somebody please chime-in.