1. to roll up logs you need a database that has been backed up and is in a dirty state, i.e. has never had the logs rolled up.

2. Log rollup is a one and done solution, i.e. Lets say you have 100 logs and a dirty/backed up DB that is eligible for log roll up.  But lets say you want to only roll up the first 50 logs.  You can do this assuming you have all 50 logs available sequentially.  However once you complete rolling the 50 logs you are done in that you cannot then tell it to rollup logs 51-100.   To actually rollup logs 51-100 you would first need to roll back/Restore the EDB to the dirty/backed up state and then roll logs 1-100.

3. As far as log sequence you cannot skip logs, so again if you have logs 1-100 and lets say log 74 was missing or corrupt then you can ONLY roll logs 1-73

So based upon the available information the answer would be that you would need to restore the last known good EDB backup to disk using RSG but tell the process to NOT Roll up or attempt to mount the DB.  The DB restore will include some logs as well and you will need to add in all logs sequentially from that point forward and the do the rollup.