You indicate that sigma_tot is 35 x 6, and fun uses sigma_tot so fun returns a 35 x 6 matrix.
Integral2 can only integrate scalar functions.
"The function fun must accept two arrays of the same size and return an array of corresponding values. It must perform element-wise operations."
To operate over the entire sigma_tot array to get a 35 x 6 output, you will need to arrayfun over sigma_tot:
fun = @(lx,ly, sigtot) exp ( - ((lx.^2 + ly.^2)./(2*sigtot.^2)));
int_i = arrayfun(@(sigtot) integral2( @(x,y) fun(x,y,sigtot),0,lxx,0,lyy), sigma_tot);
