If you do

l = 0.; k = 0; m = 1; Plot[MeijerG[{{2 - l + s}, {}}, 
{{0, 2 + k - l + s, 3 + k - l + s, 2 + k - l + m + s}, {}}, 30], {s, -0.1, 0.1}]

you see that at l=0 && s=0 the function is not defined. There may be other places in parameter space where this is also the case.

If you do

l = 0.; k = 0; m = 1; Plot[MeijerG[{{2 - l + s}, {}}, 
{{0, 2 + k - l + s, 3 + k - l + s, 2 + k - l + m + s}, {}}, 30], {s, -0.1, 0.1}]

you see that at l=0 && s=0 the function is not defined. There may be other places in parameter space where this is also the case (see Wikipedia entry for MeijerG).