chev LS motors are heavy (gen III), a lexus motor wouldn't be too much heavier than a 1.8 especially if you remove all the accessories
A guy in NZ has done it, go to
http://www.lextreme.com/ and search the forum for MX5. He ran 13s quarters on the stock motor and ecu, which is not bad

You would need to fab engine mounts, gearbox mounts, tail shaft, diff mounts. Need to throw away PPF, you'll need a bell housing adaptor, gearbox, diff, may need to mod shifter to line up properly through the hole in the tunnel etc etc etc etc etc etc etc etc etc etc etc etc etc etc etc...
A lot of work, wouldn't consider it unless you're good at fabrication or can afford to pay someone to do it. Would be an insane car though
Good luck.