Exiting T3 arrivals after baggage collection it is a 10 minute walk to T1 departures, passing through the shopping concourse before coming to the check-in desks. It's not a well used route, but easy enough to follow.

At T1 the LH Business desk is first after the departure concourse on the right as you walk out to the main check-in hall, which is convenient. T1 security queues can be busy with budget / package airline holidaymakers clogging the system. A Fast Lane sticker from LH on your BP will get you through priority security channel much more quickly.

It's only a short walk from security to the LH gates. But if you have time, you can go via the upstairs Serviceair contract lounge, which overlooks the LH gates. I've found LH flights board 10-15 minutes before scheduled departure. The lounge will call flights.

1 hr 40 should be ok, if the incoming BD flight is on time. (It's certainly better than the 50 mins LH regularly schedule for connections at FRA and MUC...)