What is minimal LO level for shottky diode mixer at 10GHz?

Regardless of incoming signal power, assume incoming power can be any necessary value. At wich point diode mixer will perform badly? about -20dBm?

LO input power of a mixer depends on its design. -20 dBm is rather referred to the RF input, LO input is typically +10 dBm or more for a good mixer. Check "www.minicircuits.com" about their mixers. With ZBS Schottky diodes, some mixers can operate with +3 dBm LO input, but a higher LO input is always preferred.
DC-biased mixers allow to use LO inputs ~0 dBm which is an advantage at mm waves where LO sources are expensive.

You must check the datasheet of the mixer that you are using to.It will write for example. Level 7 ..means that, this mixer works good, if you use at LO input +7dbm. Maybe it will write exactly the LO power needed. But be careful. If you do not supply the mixer with the power that datasheet said, you will have problems and the conversion loss of the mixer between RFinput and IFoutput for a downconverting mixer, will change.