Change length of varchar on live prod table
If you are increasing it to varchar(100 - 8000) (i.e. anything other than varchar(max)) and you are doing this through TSQL rather than the SSMS GUI

ALTER TABLE YourTable ALTER COLUMN YourCol varchar(200) [NOT] NULL


and not altering column nullability from NULL to NOT NULL (which would lock the table while all rows are validated and potentially written to) or from  NOT NULL to NULL in some circumstances then this is a quick metadata only change. It might need to wait for a SCH-M lock on the table but once it acquires that the change will be pretty much instant.

One caveat to be aware of is that during the wait for a SCH-M lock other queries will be blocked rather than jump the queue ahead of it so you might want to consider adding a SET LOCK_TIMEOUT first.

Also make sure in the ALTER TABLE statement you explicitly specify NOT NULL if that is the original column state as otherwise the column will be changed to allow NULL.