mogorzalek,
I don't think your question is properly defined. L/D is associated with angle of attack. Generally speaking, L/D increases with angle of attack up to stalling angle of attack. The maximum L/D will be reached around of the beginning of stall. However, the conclusion is based on the condition that flight speed is less than sound.
Super-sonic flight is dramatically different from sub-sonic. According to 2-D linear classic aerodynamic theory, except for additional drag, the thickness and curvature don't generate lift in supersonic flowfields. This is totally different from sub-sonic. This is why all supersonic aircraft are thin and sharp, especially for the wing. Only angle of attack can create lift. One thin flat plate is a perfect supersonic shape.
For supersonic flight, actual flight angle of attack is very small. The aerodynamic loads (both drag and lift) sharply increase due to shock wave and because the load is proposional to (speed)^2. Very little angle of attack can provide enough lift to overcome the gravity. In supersonic flight, lift is not a demand. To overcome drag is every thing, very very important.
For supersonic flight, L/D is not important. The reasons are (1) design theory is totally different from subsonic. The major thing is to reduce drag D with proper pay-volume. (2) L/D will increase with angle of attack. Supersonic aircraft will never reach the stall/flow separation angle, value of which is significantly higher than subsonic (about 12 degrees for subsonic). Before reach that angle, the aircraft would have already been structurely destoried by too much number of gravity.
Therefore, when people talk about maximum L/D, it usually means the flight is under the condition of subsonic flight or that aircraft wing is under subsonic leading-edge.