I was in a similar situation with keys.
I learned that there are 2 length blanks available.
I bought a number of old Lexus keys from Ebay.
I also learned that my W Reg 2000 LS400 required the transmitter pack with triangular indent.
These are readily available on Ebay... This one is currently under £20
https://www.ebay.co.uk/itm/2003-Lexus-gs300-is200-3-button-1512v-3-button-Remote-Key-working-part/402441486730
Once the key is cut, all that is required is the "pedal dance" outlined in many places on this forum.
I managed to lock my keys in the boot last year whilst working in Scotland. After removing a wet jacket and leggings I closed the boot lid immediately realising what I'd done!
I tried calling the wife and getting her to operate the spare key in Hampshire, whilst holding the phone in various places along the windscreen - no luck!
The AA man spent an hour trying to access the car, and once calling a colleague for advice, took the advice and gave up.
My saviour was by way of a local auto locksmith. On the Monday morning he retrieved the key code from Lexus Central (I was able to confirm it's pedigree and date of registration)
He arrived in the muddy field with a blank, typed in the code to his automated key cutter and I was able to gain access to the boot and my regular key set from the wet coat. Alarms blazing.
Charge was £86 which I didn't think was extortionate.