Yesterday Roman found a little bird whose luck, alas, had run out. Bless his little soul. Note: Finding something dead on the ground is not "catching". You can only catch living things. You can also say he came across a little bird he discovered... he happed upon... he caught sight of... he noticed...

Yesterday Roman caught a little bird but he was not lucky enough to survive.

Yesterday Roman caught a little bird but it must have been out luck because it was already dead.

Yesterday Roman caught a little bird.It wasn’t lucky because it was dead.