The 30-year-old Neath-Swansea Ospreys forward was called up following a weekend when the Lions lost captain Brian O'Driscoll, flanker Richard Hill and centre Tom Shanklin through injuries, and second-row Grewcock to suspension.
Cockbain, a key figure during Wales' Six Nations title-winning campaign, earns an immediate chance off the bench against Manawatu in Palmerston North on Tuesday as he will link up with the Lions from Australia, rather than the UK, removing any prospect of jet lag.
He will look to make the same impact as his Wales team-mate Ryan Jones, who flew out to replace Scottish international Simon Taylor and is now pushing for a Test place.
Grewcock, meanwhile, has protested his innocence after being convicted of biting an opponent and landing a two-month ban.
Grewcock's suspension will run until August 26, but he effectively only misses a maximum of four games, including the second and third Tests against the All Blacks. He was cited for allegedly biting hooker Keven Mealamu's finger.
"I do not agree with the decision, because as I argued to the hearing, I did not bite the player at all," insisted Grewcock.
"But I have to accept the decision, and that means for me the tour is over. I have decided, therefore, that I will return home as soon as I can."