Arbitration

YES you can refer the dispute to the named sole arbitrator.  If not on limitation, the suit could have been dismissed under arbitration and conciliation act 1996 and matter referred to Sole Arbitrator, because the arbitration agreement bars the jurisdiction of iil courts.

If the suit is limitation barred, wouldn't the arbitration be also limitation barred.

The query is silent on the point of start of cause of action.  If the cause of action is continuing then matter can be referred to named Arbitrator.  The limitation was applied to the suit of other brother and not to the client of Saurabh.  Cause of action for Saurabh's client is different from the cause of action and limitation for other brother.  Even otherwise the limitaion can be got condoned on the ground of having pursued the matter before wrong forum, if facts allow.

The query doesn't indicate that Saurabh's client's brother filed any suit. As regards the cause of action, from the facts given it appears that the cause of action remains same for the suit as well as for the arbitration.

well my client filled suit for cancellation first in 2004 and withdraw the same in 2007..then in 2007 filled suit for specific performance and which was dismissed for limitation in 2012...

my client paid the liability in 2009 itslef which is worth rs 7 crores... no more liability is need to paid now