Lords - I find it neither stuffy nor particularly formal - is a fabulous place to watch a Test Match. Have him buy one of the fairly cheap, available at the ground on the day, special radios so he can hear the commentary in one ear. It really helps.
There were once tours available of the museum, and perhaps the Long Room (but maybe not, I've been in there but that was with a Member, a county and England player of previous generations, unfortunately gone from this plane now, and I was there when Brian Lara hit a series of consecutive sixes) and the ground itself is magnificent. Be sure that your son knows about the slope and its influence in the match.
I prefer to be close to square of the wicket so as be able to see all the action (or lack of it) at both ends.
Test matches are good for the stomach as well as the soul. They will stop promptly for lunch, and again for tea, and these breaks are useful for the fans too.
While pretty much anything goes in clothing at Lords from caps and ties and blazers in the colours of Lords for the members, to shorts and short sleeves for the public and anything in between, Lords is one of the only grounds to both ban fancy dress, and enforce the ban strictly. So you won't see the Dickie Bird groups of 15 or more, or the penguins, or the kiwi costumes. You also won't see the giant snakes of beer glasses, or any of that guff. You won't hear the drums and whistles of the West Indies/Pakistan/India/Bangladesh if they are playing. But you will hear the polite riffle of applause after balls well hit, and a few shouts of glee as a wicket falls. But - generally - polite.
Both go, and enjoy....
But do remember that of the two teams, the winner is often the weather.