I'm going to be in Rome for the months of December and January. I'm looking for an indoor pool for lap swimming. Would anyone know of one that is in reasonably easy reach from the historic center of the city

www.hrs.de lists 43 hotels in Rome with swimming pool in Rome, however the search function does not differentiate between outdoor and indoor pool. But if you click on the hotel amenities, it displays whether it is an outdoor or indoor pool (or both). At least, you will have a choice of hotels with indoor pools in various price ranges.

Not sure how receptive a hotel would be to non-guest swimmers.

This sports club is near Borghese gardens; there is at least one indoor pool:

http://www.romansportcenter.com/

I use www.swimmersguide.com to find pools when I travel. They list about 50 lap pools in Rome. Not all allow visitor access, but for 2mo you may be able to make arrangements (membership).

Ouch - they report that Roman Sports Center near Borghese gardens charges 20 Euro for a visitor.