Can lemon juice cook raw egg?

No, lemon juice cannot cook a raw egg.

To cook an egg, the temperature must be high enough to cause the egg proteins to coagulate. However, lemon juice is acidic, and it will denature the egg proteins rather than coagulate them. This means that the egg will become firm and rubbery, but it will not be safe to eat unless cooked to a higher temperature.

You will notice that egg white turns opaque (white) when subjected to heat; this is called protein coagulation. Lemon juice will also make egg whites turn opaque, but by causing the proteins to chemically denature, not by raising the temperature.