The LSN chain is not dependent on a full backup - the only thing affected by the full backup is a differential backup which is dependent on the latest full backup.
The only way that error occurs is if you have not restored all available transaction log backups up to the current point in time since the full backup you restored to the secondary. It is highly likely that either you are not restoring all available transaction log backups - or some other process is performing additional transaction log backups that you are not aware of...
check the backup history in MSDB to see if there are any other processes performing backups.