Question: I have a SQL Server 2012 database that must be always in 'standby' mode because I must restore transaction logs from a vendor database to my local database on stand by restoring option.

It has been around 3 months since I started to download log backups from vendor's sFTP server and restore everyday to my database (in standby mode). Today, in the middle of restoring, SSMS crashed and the application closed immediately, which left the database in restoring mode.

I don't want to work all over again from the beginning. How can I change the database to standby mode and keep the sequence of LSNs; from the last LSN restored to next LSN of log backup file?

My database has no log shipping configuration between two servers, it is just a target database.

Answer: 
The way I solved is (in case it helps others): I first identified the last log file restored from the database properties (shows by date) and continued to restore on standby mode starting from the last log file then works perfect!
There are a few details that are missing from your description of the problem. For example, are you restoring using SSMS to restore the transaction logs? 

It would probably be better to create a process to periodically restore the transaction logs that have not been restored. You can, of course, schedule the times that you want to restore. 

For issues that you may face, see the following posts:

[Log Shipping Why Would You Choose No Recovery Mode](https://stackoverflow.com/questions/14447847/log-shipping-why-would-you-choose) 

[Can SQL Server database be changed from NoRecovery to Standby?](https://dba.stackexchange.com/questions/119468/can-sql-server-database-be-changed-from-norecovery-to-standby/119473)

These posts have some overlap, but read them both to get a better understanding of the options that you have.