Lambert played for the Switzerland coach at Dortmund.
Hitzfeld admits he is impressed by Lambert's achievements and says he is still in touch with his protege.
"I have always followed Paul since he left Dortmund, and I congratulated him on his promotion to the Premier League," said Hitzfeld.
"Paul answered me immediately. As a player he always thought like a coach. He was a leader.
"He didn't cost a fortune when I bought him, and no-one expected him to become a key player - but he did. So it is no surprise [that he has become a successful manager]."