This is not a good idea. You need a minipage only for the caption, not for the "float". Otherwise it makes no sense, because the tabular may be of a larger size than the minipage and then the tabular is not horizontally centered.
I have tried the method suggested by you, but I get compiling errors. The LyX file is enclosed.
attached the correct file. With right mouse button clicking on the minipage button you can change the width of the minipage. I set it to 30% of columnwidth.
Herbert
#LyX 1.3 created this file. For more info see http://www.lyx.org/ \lyxformat 221 \textclass article \language english \inputencoding auto \fontscheme default \graphics default \paperfontsize 12 \spacing single \papersize a4paper \paperpackage a4 \use_geometry 0 \use_amsmath 1 \use_natbib 0 \use_numerical_citations 0 \paperorientation portrait \secnumdepth 3 \tocdepth 3 \paragraph_separation indent \defskip medskip \quotes_language english \quotes_times 2 \papercolumns 1 \papersides 1 \paperpagestyle default
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\end_inset
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\align center
\begin_inset Minipage
position 1
inner_position 0
height "0"
width "30col%"
collapsed true
\layout Caption
Table for both dice (
\begin_inset Formula $D_{1}$ e $D_{2}$
\end_inset
).
\end_inset
\end_inset
\layout Standard
blah
\the_end
