EDIT: Wait a minute. No individual stocks are listed yet on LTSE https://news.ycombinator.com/item?id=24421925 so what am I supposed to ask them to do?
When I want to buy a share, the first thing the brokerage asks me is the stock's symbol. Without any listings, what am I supposed to tell them?
So if you want to trade any US exchange-listed symbol, your broker can do that on LTSE (assuming they are a member)
Or maybe the point is: there's no point in buying shares with LTSE today, even though you technically can do so, and instead I should wait until there are individual listings and buy those?
(And even then, I don't need to use LTSE, I can just buy their shares on NASDAQ with Etrade like I always do…?)
Others allow their clients to direct orders using a specific trading strategy. If you have a family office it's very likely this is part of the strategy.
However, ordinary retail investors are sometimes locked out of this system. I don't know Etrade's policy in particular, so I can't say for sure what you would have to do.