The lx173 is a good LAWN tractor (not designed for ground engaging implements). I have one that we use to cut the yard, places the tractor won't go, pull a small sprayer, etc. We bought it used (abused?), changed the oil, sharpened the blades and it has been pretty much problem free for several years. EXCEPT.....

It likes to jump out of reverse some times.
Your problem could be a lot of things - anything from the shift linkage needing adjustment to the transaxle being fried. Hard to tell without looking at it.
When you try to put it in forward gear, does it make a ratchety, clacking noise? The transaxle uses shift dogs (like little square keys) that slide into collars on the gears to engage them. With wear, age, use, etc, the shoulders on the gears and the profiles of the keys round off, making it pop out of gear, then eventually fail to engage at all. Usually only happens with first couple forward gears and/or reverse though. If this is the problem, can split the transaxle and replace keys and clean up/replace gears (parts are available).
OR - it was a fairly common transaxle used on a lot of different lawn tractors - just get a used one from "that online auction site." Depending on the deal, you may pick one up for $40-50. Easy bolt in/bolt out switch over.
IF you look around, you might find a whole "parts" tractor for cheap. I bought one with a blown motor for $25.00, so will eventually swap out the transaxles when my reverse becomes a problem.
The series were good well built "old style" mowers - one in decent shape would be head and shoulders above a new box store model. They would support a front mounted snowblower, tiller, and of course a mower deck.
Hope that helps!