Lufthansa and Singapore Airlines are both in the Star Alliance group and use Terminal 1, but the councourse are not shown on the Frankfurt Airport website until the flight day. You could be using Concourse B or Z for arrival and leaving from Concourse A or B. A and Z are in the same building different levels) and are for in-Schengen flights and out-of-Schengen flights respectively.
There is no security check between Z and A. Just go to the hinge of the two wings and go down through immigration (passport) to the A level. If both flights use B, you just go through immigration, not security.
If either your arrival or departure uses Concourse B and the other flight A or Z, you will have to use the SkyLine shuttle train or the tunnel to go between buildings, and there will be security when you go from the SkyLine station or the tunnel into a concourse.