I don't think you need a rail pass of this travel.
First place, a German Rail pass will not cover the entire trip. Lauterbrunnen is in Switzerland.
You would need a pass covering Switzerland from Basel to Interlaken (not sure if any pass covers (Interlaken to Lauterbrunnen). Interlaken to Salzburg might be travel only in Switzerland and Austria, although you could go through Germany for part of that trip. It's beginning to look like a more expensive, 3 country Select pass.
Salzburg to Munich can be done less expensively with a Bayern-Ticket (€20 for one person). Munich to Frankfurt can be done for as low as €29 on an ICE with a online Dauer-Spezial-Ticket.
You can also purchase online a Europa-Spezial Schweiz ticket from Baden-Baden to Interlaken Ost for €39.
Frankfurt to Baden-Baden can be done fastest by ICE (probably advisable since you will have just arrived with jetlag) for €42. You can also take an S-Bahn (local RMV ticket, €3,70) to Mainz and use €19 Rheinland-Pfalz-Ticket Single to Karlsruhe. From Karlsruhe you would need a local (KVV)ticket, for €5,20, to Baden-Baden.