Hi OP. This 'activities half day' is a new thing. But, as in other schools, they will be looking for 'teachability' and engagement, rather than getting something wrong or right.
My DS went right through that school so a long time since he was interviewed! But there was some kind of abstract puzzle and a passage to read and then answer a few questions on.
One thing I would say is that the interview process is as much about schools trying to gauge who would actually take up the places if offered. So, if possible, try to encourage your son to tell them that - eg. if they ask him if he has any questions or what other school he has applied to, tell them "if I am offered a place her I will definitely take it." Make it easy for them - don't leave them guessing! They want to offer places to the ones who want it most! None of these schools want to be someone's back up option.
General questions that frequently come up -
Why do you want to come to Latymer? (He should try to say something personal and specific, rather than just, "I like it." Maybe something about sports there if he's that way inclined? Or that he prefers co-ed? Just something that makes sense to him - even a random thing.
What are you reading?
What are your favourite subjects?
LU is different to other schools, I think, in the sense that it is very "global" in its outlook. They may well ask about a topic in the news. Or an environmental issue. They teach their own subject called "World Perspectives" and this is quite central to the ethos of the school. It's largely about sustainability and global warming issues, with a bit of relevant politics and economics thrown in. So just talk to him a bit about the current strikes; cost of living crisis; a few environmental issues; the general situation in Ukraine (at a basic level); who the PM is, etc. Just in case!
One question that came up for my kids at various schools was - "if you had a day where you could do anything at all, what would you do? Or "if you could go back in time to meet your great great grandmother, what would you tell her / how would you explain the internet to her?"
My DD (at another school) was asked, "Which is more important - money or happiness?" I remember her also being asked - "What gives money it's value?" That was not at LU, I think it was either G&L or SPGS. But just to give an idea.
But mainly, just be keen about the school. My DS actually said something along the lines of, "I've had interviews for Hampton and St Paul's but the people here just seem more like me and I feel like if I come here I can be anything I want to be, so if I'm offered a place I will definitely take it straight away."