The ones he's in are from 15 to 40lb so should be plenty big enough for him, I always makes sure the frilly bit is fully out and his willy is pointing down otherwise it goes up his back. None of the nappies seem to work, unless he just poos a weeks worth of poo every time! He hasn't done a poo in the lidl ones yet so can't say what they'll be like for poo but not holding out much hope as they won't even hold his wee!
Best nappy by far for leaky poos is pampers new baby. They go up to size 3 and although expensive you save loads as they don't need changing so often (wees) and fewer clothes ruined. The other pampers brands aren't as good but pampers baby dry are as good as asda for poos but better than them for wees.
We use Aldi mamia for day time and Pampers baby dry for night (find they holds a little more wee than Aldi's do) and haven't had leakages apart from when we moved up to size 4 when DS hit 16lb (which are the 15-40 lb you've mentioned I think?) we actually went back to size 3 for another month and he was fine. I think the size 4 covers such a big weight range they were too loose on him.
Seconding cloth nappies here! they contain even the biggest poos. They have changed a lot since the old Terry squares (although we sometimes use them!) Have a look online you can get some really lovely patterned ones.
I've changed back to morrisons just now after using aldi first then asdas. I've never liked pampers. Also I get staff discount as my mil works there. I also use cloth pockets, and after watching a YouTube video they work well. But ds poos first thing in the morning when he's still in a disposable from night.