Been following this one and the other problem you have, probably as big as the postcode lottery, is no driving history. You don't have any NCB to your name. The down side of the "get the insurance in someone else's name and be a named driver", admittedly some insurers now take this into account.
My step son (19 with 3 years NCB including a scooter @ 16) has a little Corsa. Our postcode area rates low risk, he has no mods and pays about the same sort of amount in insurance as you are being quoted for the Lex. Balance it out and I think that you will find it hard to get a lot lower on the quotes