The L110 Auto has the hydrostatic transmission and final drive all in one piece. This is what it looks like:
[Linked Image]

The unit is probably a TuffTorq K46 - this can be verified by looking at the unit's identification plate. I have read that another brand of transmission was also used as an alternative in that mower.

You can read the owner manual here:
http://manuals.deere.com/cceomview/OMGX21647_K3/Output/Index.html

The manual says the transmission is a sealed unit, not owner-serviceable. Various internet reports say that JD dealers simply replace them when they blow up, as your neighbour's seems to have done. (It seems this is not an uncommon event for K46 transmissions.) This is very expensive for any hydrostatic transmission, and for an 8 to 10 year old L110 will probably not be financially viable. If you or someone nearby really likes to get on the spanners, you might consider buying parts and rebuilding the unit. Here is some information on that approach, if it is a K46:
http://www.tractorbynet.com/forums/parts-repairs/164892-tufftorq-k46-repair-guide-pictures.html

You now see one of the reasons why I rather like the Greenfield's type of transmission, and generally regard hydrostatic units as best left for commercial operators. The L110 Automatic may have been an example of what happens when you try to make a consumer product with advanced features, and you do it by using short-life componentry.