There is a really easy way to tell if the meth lab spawns on the Moretta. There are several locations on the map where open cardboard boxes with the various ingredients spawn (the exact same kind that spawn in the meth lab on Hotline Miami Day 1). These boxes only spawn if the meth lab is on board the Moretta. Ingredients WILL NOT spawn in the wooden crates that need a crowbar, only in the cardboard boxes.
http://vignette4.wikia.nocookie.net/payday/images/8/8a/Docky...This is a map of the dockyard with the potential ingredient spawns marked and a map of the keycard spawns as well (Credit for the first picture goes to Ktash on stackexchange.com, thanks bro! The second comes from the Payday wiki).
I've heard from players on the PC version when I still played it actively that there is a ridiculously small chance that even if there are no ingredients on the map at all that the lab can spawn, but I personally have never seen this playing the mission dozens of times so I can't speak to the truth of that.
I'd recommend stealth for this mission if you can manage it, since fighting enemies is by default more difficult than fighting no enemies. The worst thing in stealth is waiting for the ship to make it to dock lol. My best time for stepping foot on the Moretta itself in steath is around 15 minutes, and my loud times easily broke that time, but then again I love stealthing jobs in Payday. Besides, 400 second hacks are the devil. But stealth vs. loud will just come down to play style I guess, it doesn't truly make a difference either way.