Morning @[deleted],
Yes it is possible to sync a rhythm app to GTL in the way you have suggested. I'm not familiar with Lumbeats Rock Drummer but it's important to make sure it's reporting the phase to Ableton Link. This is the number of bars in the drum sequence. It could be a manual setting which you would set to 16 bars or it could be handled automatically. If Rock Drummer is reporting the 16 bar phase to Ableton Link then other app can synchronise with this and start playing at the beginning of the sequence.
Next make sure GTL is stopped and, from a blank session, start a new 16 bar recording. Starting from a stopped GTL session allows for a 'quantised launch', basically waits until the beginning of the sequence before playing/recording. Recording 16 bars ensures that GTL has the same length sequence as Rock drummer. If you record other lengths of loops first then it is not guaranteed that the to apps will be in phase.
If you do need to record shorter loops first then go to 'Settings' -> 'Clock' and set the 'Sync Quantum' option to 16 bars. This will ensure that GTL will always quantise launches to 16 bars irrespective of the length of your first loop. Just remember to start recording from a stopped GTL session.
The latter ensures that the two apps start in phase/sync however it's still possible for GTL to fall out when switching groups. Imagine you have one group of 16 bars, perfectly in phase with Rock Drummer, then you switch to a group of 4 bars and then straight back to the first group. Now GTL will be 4 bars out of phase with Rock Drummer. The best option is to make sure all your groups have at least one 16 bar loop in . Another is to experiment with the 'Force Phase Alignment' setting in GTL. This will force all other apps in phase with GTL, so you can switch groups anytime and Rock Drummer should follow. Depending on the other app, this may or may not work well.
The last and probably easiest option is to switch CUE off in GTL. Then you can record, play and switch groups whenever you like. If you're in control then you can make sure things come in at the correct time and completely forget about Ableton Link phase alignment! This is my preferred method.