Lions head coach Sir Clive Woodward agreed to give Robinson more time with his family and predicted he will still have enough time to be in contention for the first Test against New Zealand on June 25.
"Jason is a strong family man and wants to spend as much time with Amanda as he can," said Woodward.
"This still gives him time to get out to New Zealand and make a major contribution to the tour."
Robinson usually takes his wife and children on tour with him but with the baby due in just three months he will leave them behind in June.
He said: "I have played a lot of rugby in recent months and with my wife pregnant I want to spend this time with her and the children.
"I think it is the right thing for the family, and the right preparation for me to be in the best possible shape when I get to New Zealand in early June."
Robinson missed the Lions' 25-25 draw with Argentina after leading Sale to the European Challenge Cup title on Saturday and is not the only player to be joining up with the squad late.
Both Gareth Thomas and Stephen Jones have had to delay their departures due to continuing commitments with their respective French clubs, European cup winners Toulouse and Clermont Auvergne.