Well, what you seem to be suggesting is "Did life evolve twice on Earth?"
Your original question has an answer: Probably yes. It's not unlikely to think that the original cell evolved into two different paths and then one went extinct. However, that doesn't address LUCA. If we found fossil evidence of what we thought was LUCA, and then fossil evidence that LUCA had a genetic cousin - all that would do is push the application of the term "LUCA" on more evolutionary step backwards until both shared a common ancestor which would then be called LUCA. You can do this indefinitely until all life originates from a single cell, with countless offshoots which have gone extinct.
If you mean was there a whole other type of life - one that did not originate from LUCA and existed - then the best answer we have right now is "No." All life we know of, no matter how different and old, is still based on RNA/DNA and proteins. Fossil evidence supports this premise until about 3.5 BYA.
If there was an 'alternate' construction of life, we have not found the fossil evidence for it, and might not know what it was if we did. If the alternate form didn't utilize cells, we might not be aware we had it. If it did, but utilized different metabolisms or structures for proteins and storage - that evidence would be long gone by now.
Our best bet for answering if life can evolve differently than what we have today is out among the stars.