I have not kept-up with the more recent Lehman belt drive designs, but I believe they are oil filled...not sure. The early Lehman kits had grease filled diffys and there is a grease zerk on the differential and is suppose to get a shot every 2,000 miles or so. My experience with these is that they don't need to be greased that often. The more grease you put in simply squirts out past the axle where it slides through the bearing race into the diffy. I generally give mine a couple of shots every 10,000 miles or so, which has been about once a year. I have had those differentials apart and have never found one dry.
I feel like if there is a grease zerk on there....then it's there for a reason. Maybe they simply grease/lube them at assembly and don't recommend anything beyond that? I am sure some of the other TG owners will chime in with an opinion....or just ask your dealer.
Belt tension is about the same on any trike. You have to get both rear wheels off the ground (remove the wheels) and each side has 4 bolts that will have to be loosened. These bolts "clamp" the rear axle to the swing arm over some studs (for lack of a better word). Loosen those up. You should see an adjustment bolt on each side that will push the axle assembly rearward as you turn the bolt. Adjust both at the same time in very small increments and measure the exposed threads to make sure they are equal. A little goes a long way. If you need to loosen the rear to get some belt slack, the process is reversed, but you will have to "tap" the rear axle inward toward the swing arm after you loosen the adjuster bolt. Again...a little adjustment goes a long way. There are also some adjustments that move the axle left-to-right and you should not have to fool with those. It's not an easy proposition. If you get one side far enough out of whack...the belt/pulley alignment will be affected. The best way is to get it up where you can lay on your back under there and check the belt alignment after you have made the tension adjustment to make sure it is running true on both the front and rear pulleys. It can be a real PITA. When you move the adjustment bolts after you have loosened the retention bolts (clamps) and tighten those all up again...it will cause the tension adjustment to be slightly different once it's all torqued back down. The best thing to do is loosen the clamping bolts "only enough" to be able to move the axle back with the adjuster bolt.
It's like a dance....lots of things have to move together and you may have to do it a time-or-two to get it right. Get ready to spend a half-a-day to do it, or....take it to your dealer and then take your chances on whether they do it right or not.
I have done it enough to be able to perform adjustments without jacking it up, or removing the rear wheels, but you need to have performed the adjustment enough times to be able to do that.