Dear Alexey, 
     it depends a lot on what you would like to measure. If you are planning to 
make very accurate measurements to detect either photophysical properties 
of the fluorophores or intermolecular distances, additional heterogeneities in 
the lifetime decay are a problem.

If you would like to measure FRET / no FRET (interaction / no interaction, just 
simplifying) more complex decays are not a big problem (within limits). Notably, 
in a typical FRET experiment you would anyway measure multi-exponential 
decays because of a mixture of non-interacting donors and may be also donor-
acceptor pairs that are interacting in different ways. On the top of this, there 
is also the possibility of non purely single exponential decays of the 
unperturbed fluorophore. Consider that often we are not capable to detect 
multi exponential decays because we do not have enough signal-to-noise ratio 
to start with.

Occasionally, fixing and mounting could be even beneficial because of the 
improved optical properties of the sample and, when using some anti-fading 
agent, less photobleaching. However, fixing and mounting will introduce 
differences in the biochemical environment of the fluorophore which could, in 
principle, even suppress any FRET: this is not a rule.

In general, FRET on fixed samples does work (there is no physical reason why 
it should not), but could add some nuances that can/should be dealt with.

Last remark. Fixing and mounting can alter the localization of proteins and 
cause false positive or false negative FRET: good control experiments are 
always necessary (in any case). 

Cheers, 

Alessandro Esposito
University of Cambridge
www.quantitative-microscopy.org