LCR is the fastest method of recovering the log file in non-clistered Mailbox roles. CCR is with very similar and more advanced feature to reduce the down-time even more appreciated then the traditional cluster.
If there was Local Continuous Replication (LCR) enabled on the server, then you may recover the deleted log file from the LCR copy.
For more information
Demystifying the Local Continuous Replication (LCR) feature
http://www.msexchange.org/tutorials/Demystifying-Local-Continuous-Replication-LCR.htmlIf CCR/LCR is not enabled, then the option will be to restore the DB from backup and only keep the log files generated before the deleted log file and replay them. The Data of the log files after the deleted log file will be lost. This is safer than running a hard repair (eseutil /p, eseutil /d and ISINTEG commands)