No it is not possible to checkmate a lone king with king and Knight ...
Even a lone king king cannot be checkmated using King and a bishop...
This is because knight controls only one coloured square a a time (either black or white), this is the case with bishop....
So the opponent king can run using the other color which is not controlled. even if you control that escaping square with your king that will be stalemate (Draw)...
Even two knights and a king cannot mate a lone king (True fact)...
The minor piece combination that will mate a lone king is King + 2 bishops or King + knight + bishop....
Since two bishops control both colored squares and in case of Knight and bishop, knight should control the opposite colored square as that of the bishop ....