I believe this question is best answered by objects conservators on the
Cons DistList; see below
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I believe there is literature in the CoOL archive on this subject.  If
the Lucite box is an art object, then I would have a conservator look at
it. There may be components that should not be cleaned.  To learn how to
select a Conservator and obtain a referral contact AIC at URL:
<http://palimpsest.stanford.edu/aic/>.

If it is a vitrine, then try cleaning with Brillianize (sp?), a product
that can be bought through museum and conservation suppliers or through
your local Plexiglas supply store such as Cadillac Plastics or Tap
Plastics.

Timothy Vitale
Paper and Photograph Conservator
& Preservation Consultant