\documentclass{article}
\begin{document}
\directlua{
a= % initial data
{{1, 2, 3},
{10,11,12}
}
a[3]={} % new row
for i =1,3 do
a[3][i]=a[1][i]+a[2][i] % calculation
end
labs={'x','y','x+y'}
}
\begin{tabular}{lrrr}
\directlua{
for i,v in ipairs(a) do
print('\string\n== ' .. i)
for ii,vv in ipairs(v) do
tex.print('&' .. vv)
end
tex.print('\string\\\string\\')
end
}
\end{tabular}
\end{document}