Dear Professor,
Thank you very much for all your kindness and valuable help to us.

Yes, I have tried without iterative solver and it does not work.
Please find input file and mesh in the attachment. I include two input file and removing iterative solver. One corresponds to penalty method which works fine and next one corresponds to Lagrange multiplier which it does not work. To make it clear, the difference between two input file are as follows:
ilagrange ipenalty
=============================================
TIED 1 2 4 NTOS 1 2
SOLM LAGM SOLM PENAlty 1.E+05
block segment FACEts
Again, very much for all your help and kind answer.

Best wishes