Makita and Dolmar merged. Call them Dolkita. Makita BCM2310 should be similar. Search ebay for Makita BCM2310 Gas String Trimmer carburetor carb part KK21044AA. Compare it to your carb.
I'd stay away unless you can perform at least moderate wrenching yourself. IPL shows Hydro Gear 321-0510. It may be totally shot. A new one is $600+. I'd bet it's an entry level unit that doesn't like slopes or towing at all.
Figure out which line is which. Open the cap, dump fuel, look in tank. Use a bent coat hanger to pull line to tank opening. Is a fuel pickup (filter) attached or floating free in there? Either the blue line is the fuel supply w/ pickup on end or purge return line with just a short line connector...
If starter and brakes fixed, I'd shoot for $300...touting the Peerless 920 geared transaxle. I'd rather have your LT than anything outside Lowes/HD/Wally. But I like geared trannys.