That's not a bug in LyX, it's a restriction in TeX. You cannot use an eqnarray 
environment inside a cell of type c, l or r. \parbox or a minipage environment 
is required, or a p column (or b, m with the array package).
Fix with LyX: insert a box (minipage). Possible fix in the exported TeX file 
for instance with a column of type p instead of c: 

\begin{tabular}{|c|p{4cm}|}
\hline 
 & \tabularnewline
\hline
\hline 
 & \begin{eqnarray*}
a & = & b\\
 & = & b\end{eqnarray*}
\tabularnewline
\hline
\end{tabular}

Btw. it would be better to use an align environment instead of eqnarray,
for an explanation you may look at: http://texblog.net/latex-
archive/maths/eqnarray-align-environment/


** Changed in: lyx (Ubuntu)
       Status: New => Invalid

-- 
any multiline equation inside a table in Lyx 1.50 breaks
https://bugs.launchpad.net/bugs/151110
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