The reason LH is doing well from Liverpool is, no competition from Easyjet or Ryanair on point to point to Frankfurt, no other hub airline, when KLM tried , Easyjet jumped on them. They were the incumbent and known better than KLM in the Liverpool City Region ( You could argue if KLM had linked Liverpool years ago like other regional centres, it would have been different), plus Liverpool is known worldwide, its famous, so Lufthansa are tapping into this, bringing in inbound tourists. The service is to go daily except Saturday in March. I suggest the best way forward is double daily, and not addition of KLM.Something to consider is that Lufthansa will be looking for a decent number of connecting passengers on a particular route before launching a new service.
Whilst Leeds has Aer Lingus to Dublin and KLM to Amsterdam, Liverpool has been without a connection to a European and/or UK hub in over a decade now.
A quick look at available seats for next week shows that from LBA, EI & KL have just over 4600 seats available, whereas at LPL, LH only has just under 500 seats available.
Simply put, at Liverpool there is no direct competition to Lufthansa flights, whereas at Leeds there are already 2 airlines competing for connecting passengers.