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.
Paul
#LyX 1.3 created this file. For more info see http://www.lyx.org/ \lyxformat 221 \textclass report \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
\layout Standard
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placement H
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\layout Standard
\noindent \align center
\begin_inset Tabular
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status Open
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\backslash
begin{minipage}
\layout Standard
Table for both dice ($D_1$ e $D_2$).
\layout Standard
\backslash
end{minipage}
\end_inset
\end_inset
\the_end
