Well... *live* might be harder than you envisage. That being said...
I'd crack open obdgpslogger's code, and set journal_mode to WAL [so that concurrent writing and reading doesn't cause heartache]:
[just use sqlite3_exec shortly after the db successfully opens].
I'm not sure, but you may need to drop in a version of sqlite3 that's 3.7 or later [can't remember what's included in the source, offhand]. If your system has sqlite3 3.7 or later, there's a cmake compilation flag to use the system sqlite3 instaead of the one included
Then I'd use obd2csv occasionally [or some other custom-written tool for the job] to dump the database to a file that I could upload to the server. One simple script could do that.
Or, I might insert code into obdgpslogger that uses the backup api to make an entire copy of the current database occasionally while running, and have a script copying that file up to a server where it could be postprocessed.
Basically, if it were me, I'd use obdgpslogger as-is [or almost as-is], and "occasionally" [10 seconds/30 seconds/5 minutes/whatever] take a copy of the existing database via either a script or a combination script + modification to obdgpslogger, and do my own processing on the server.