Yesterday we could manage to backup transaction log from only a .ldf file as:
1-Created a new dummy database
2-Stop SQL service
3-Replace the dummy database's .ldf with our .ldf, (put to the same path with same name)
4-Start SQL service
5-Backup Log [DummyDB] to disk='...' with no_truncate
This log backup saved us the last one day's data, because last full backup was overnight,
It worked for us..
Regards