Why does Lawnflite Lawn Tractor motor stop when deck is lowered?

Your safety switch on the seat is probably not functioning correctly. The mower can't tell that there is someone seated on the seat and therefore when the deck is engaged it shuts the engine off for safety. Look under the seat for a plug with two wires. That is the safety switch. There are two common switches. Normally open and normally closed. To test it you can unplug the switch. If the mower works with it unplugged you have found the problem and need to replace the switch. If it does not make any difference use a small piece of wire to jump across the plug at the end of the wiring. If the mower works with it jumped, again replace the switch. If neither of these make a difference then the problem must be in the wiring.