Sorry. At the end of the deck engagement lever/shaft there is an arm which was made of cast aluminium. The casting simply broke. I found the part number (GX21041) on line and bought the replacement at my local dealer (about $5). You can see a picture of it here
John Deere Model LA120 Lawn Tractor Parts, Page 2. The new part is made of steel, so JD has realized the original part was bad design. Very easy to replace.
I really like this mower, and I'm sure it'll being doing the job for years to come.