Q.Which document contains the complete list of LSA/FFA that requires shore servicing? e.g. annual, two-yearly, every 5yrs?

There is no such document because some of the requirements change as per the flag.

For example, one flag may have the requirement for annual shore servicing of the Fire extinguishers and other flag states may require that the annual servicing can be performed by the ship staff.

So while some requirements set by the IMO regarding servicing of the LSA FFA are straight forward, many requirements ask the flag states to define the conditions.

The best place to look for these requirements is the checklist (or PMS) of the company and/or any flag circular from the flag of the ship with this regard.   

You should check the SOLAS, LSA , FFE publication regarding to servicing time and which services will be applied.