I believe you can send in your application then add to it once it has been received. I remember I worked fora guy a few months after applying in November and he wrote me a letter of recommendation that was added 4 months after I applied. I would call the individual schools and ask if it is ok, but I am 99% sure it is. You can apply without having taken the LSAT and add or modify the score later so I don't see why it would be different for an LOR. Again, check with the school I am just some random guy on the internet.