Simaudio MOON 610LP with Lyra Kleos

Is it humming or hissing? Because these are completely unrelated. And just a heads up, you will not be able to get rid of the hissing noise.

It’s more humming than hissing. And while we are st it, what’s the difference in the source and why it won’t go away?

60Hz hum is usually improper grounding or due to a ground loop. Not easy to solve. Make sure that the cartridge leads are snug. Tonearm has ground continuity all the way to the ground post. You may even try disconnecting the ground cable entirely as a test. 

There may be another component in the system that is causing a ground loop. Cable box is a very common culprit. Light dimmers. And just about everything else.

Hissing is input noise from the OP amplifier. In your case I believe it's a National part, LM4562. It's very low noise, but some hiss will be audible if the preamplifier's volume is turned up and no record is playing. There are quieter designs using discrete jfet inputs. 

When did this problem become evident? How long have you had these components? Is the SIM’s MC gain, compatible with the LYRA?

I can assume that if your using a Kleos, in order to maximize that investment, you'd need another phonostage.