Synchronizing two databases is possible, if rather complex. You need some mechanism to find out which records have changed, and if it is possible to have new changes in both databases, you also have to resolve conflicts.
A timer-based approach doesn't sound efficient: in most cases, the timer doesn't have anything to do; and after some data change, there is some amount time where the databases are not synchronized.
Can't you just replace SQLite with MS SQL Server?
I.e., have some configuration settings that determines whether your program's data lies in SQLite or on a server?
Assuming that an SQL Server database with the required structure already exist, this would, in theory, need nothing more than a changed connection string, and supplying some user name/password (if the server isn't configured to automatically use Windows logins).
There shouldn't be any big differences in the SQL dialects used. You have, of course, to test all your queries.