There are some playable old lutes, although not renaissance ones.
But first of all: Stradivari and Amati violins are still in use, although all
of them are horribly transformed into a steel string instrument to be able to
play with orchestras in large concert halls. the glue joints can be easily
fixed if they become brittle and this is also true for lutes. The drying of
the wood improves the sound in the case of violins and other string
instruments. With lutes it's slightly different. I have a recording by
Hopkinson Smith playing on a 17th century lute two suites by Gautier, but
this lute got a new top. The problem is that most lutes didn't get a proper
treatment in the past compared with famous Amati/Stradivari instruments. I
think some of the left over instruments can become playable if a good
lutemaker spends a lot of time on such an instrument. In all cases the top
will have to be replaced. Still the sound will not be very much better or
even worse than a new instrument, so it will be just for fun to play on such
a lute.
Taco Walstra