Take the battery out so you can really get into the area in front of the battery to give the linkage pivot points a good covering of some light grease or as was already mentioned, some white lithium grease, it sticks on the surface and stays put. I'd even spray it on the notches the lever engages into. Then to make sure it is doing any improvement, work the gear shift lever back and forth and work it until you see improvement. It might require the use of some penetrating oil at first if it is really bound up.
I had one with no grease in the transaxle. Remove the 4 screws holding the back plate and look on the left side top of transaxle is a black rubber plug. I worked it out, an added 20 50 oil to soften the grease that gets dryed out to paste the oil worked great, I had to carve the rubber plug a bit to reinstall the plug. But, after adding oil and working it, the shifting loosen right up. I also had trouble getting in reverse.
the best way to get the plug in correctly is to drop the transaxle. it's really not hard. the plug will push back in with a small phillips screwdriver. the grease that it calls for is 90 weight....about 16oz. and while you have it out, grease the linkage up.