hi! no you don't need to fill out your ucas before your lnat, however oxbridge requires your ucas AND lnat by the 15th, im not sure about other dates for other unis but thats the important one considering its in 10 days lol - im assuming its the same for the others, both are due on the ucas deadline for that university.
yes, you need to choose those universities on the lnat website or it might not be sent to them / might take longer due to complications and then it might only be sent post the deadline, atp im not sure if your application is valid anymore.
if you put your ucas number on your lnat account and its accurate, it will be sent to your universities.
gl with your exam !