How would I buy a share of a company on LTSE today? Does any major online brokerage work with LTSE?
Yes, the major broker-dealers and market makers are members of the exchange. You can route orders to LTSE via your existing broker, just call them up and ask them to do so. I believe Interactive Brokers, in particular, extends this privilege to all of their retail customers. But I don't have first-hand knowledge of this, just what I've heard.
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?