Ask the agent at IAH to tag the bag through to GVA on the LX flight. You've got a pretty good chance of that working given *G status and both flights being *A metal. And you'll likely save the $$.

If they balk then you need to deal with immigration and baggage claim and check-in at LHR in the short connection window. It'll probably work but there is some risk there with the timing. If the agent in IAH won't check the bag through I'd do OLCI from IAH for the LX flight and buy the checked bag at that time. You'll also have a pretty good idea if the IAH-LHR flight looks to be on time at that point in the process.