Can I put a mortice lock on a door just 34mm thick?

Yes.

Yes.

There's no need to worry about slimline, you will be able to fit a 'standard' 5 lever mortice lock and furniture or a 5 lever deadlock (without furniture) with no problems.

Brian G

I fitted a mortice lock to a door that was of standard thickness, but had lots of glazing so that the bit of wood I was working on had a fairly small cross-section. I bought a mortice lock with an outer hardened anti-drill sleeve, and then removed the sleeve which was only held on with small bolts. I reckon that burglars are more likely to try to force the door than drill out the lock, so it was best to minimise the amount of wood removed.

Insurance companies ask whether you have 3 lever deadlocks fitted but it's obvious that, in the case of thin doors, they're worse than useless. I've just been getting a few quotes and leaving out deadlocks, burglar alarms, smoke alarms etc made very little difference to the premiums.

If the OP is concerned about the risk of burglary, I'd be tempted to replace the entire door and possibly the frame too with something more substantial. It doesn't matter how good the lock is if all it takes to gain entry is a firm kick at the door. The lock would just smash out of the surrounding timber.

That's what the steel plates are fitted to prevent.

I second David in Normandy's suggestion.