That's not a complete sentence; it doesn't have a subject. It reads somewhat like a caption for a picture. I don't think you can leave the article out, but an entire sentence (at least) would be helpful.
Meticulously recorded experimental procedures and results in lab book
Seems to me that either of the three ways works, depending on the circumstances:
Omitting articles makes it informal in the way of note-taking or conserving space.
Using the means having a specific type of lab book in mind.
Using a means referring to any type of lab book.
I agree with Gurseal. It is common in a lab report to use 'note form' or 'bullet form' which does not include a subject and misses out articles. I would say that you do not need 'a', so long as you know that if you were writing correct English the sentence would be
'I meticulously recorded experimental procedures and results in my/the lab book.'
We can't tell you which one is correct in this case, you will have to ask whoever is supervising you in the experiments which way he wants it written.