The problem is, as is shown in the LyX Wiki, that longtables do not work inside floats, and there is no possibility to give a caption inside the table. But the hack given in the mentioned LyX Wiki section does not help as soon as you define a table head, because then the line with the caption in ERT is moved below the \endhead command. Thus, you have to define the first line with the caption command as a table head. The following worked for me (created with LyX 1.6.7 on Windows). I had to shorten the table, because the example would have been too long otherwise.
#LyX 1.6.7 created this file. For more info see http://www.lyx.org/
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<row>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\family roman
\series medium
\shape up
\size normal
\emph off
\bar no
\noun off
\color none
MYH11
\end_layout
\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\family roman
\series medium
\shape up
\size normal
\emph off
\bar no
\noun off
\color none
myosin, heavy chain 11, smooth muscle
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\end_body
\end_document
This is too long for a comment, so I’ll put it in the answer:
I just realized that the caption is also shown on the second page, which it shouldn't. To change this, you can go to the table preferences in LyX and change the status in the longtable tab to “First head” instead of “Head” (the exact terms might be different, I use a German LyX). If you would like to have the caption also on subsequent pages, but with a different text, you can have two lines with the caption, one defined as “First head” and one as “Head”. For the continued caption, you have to insert a caption command with an empty optional argument, because otherwise there would be two entries in the list of tables. Thus, the ERT for the continued caption should look like this:
\caption[]{A long table (continued)}\\%
