I bought one for $50 last year that had water in the oil. If the engine, deck and transmission are in good condition it probably is worth $200. If your buying it to keep.
https://www.mytractorforum.com/12-john-deere-forum/1270186-another-dead-deere-lx178.html

Cannon

 

I'd think it's worth that. The LX series were good tractors, I don't think they had hour meters so look for wear on the tires, the deck, the seat, the foot pedals, oil leaks on the axles, does the engine smoke, white, blue or black. Looks pretty clean for a '90,s tractor, how much did the guy mow, did he plow snow, try to estimate how many hours a year he used it. Doesn't look like many from the pictures but you never know. I had an 1993 LX 172, air cooled single cylinder Kawasaki, 5 speed gear tranny, washed and waxed it regularly, mowed a half acre, plowed snow in Syracuse NY with it for 20 years and sold it for $450 3-4 years ago, can't remember exactly, I've got CRS.

 

Excellent machine. Great price! Here's what I did when my hood got totaled:

Search craigslist, ebay, wherever and find a METAL hood that will cover the engine. Weld a rod across the frame to mount the hood to pivot on. Paint is available at Lowes AND Walmart. Make certain the hood has the lights intact!
Mine is off a Craftsman GT. With the steel hood, you can run into anything you need to!
RIP ALL THAT PLASTIC OFF.