It seems a great chance for the 29-year-old Easterby, who was called-up to the tour to replace the crocked Dallaglio on Saturday, following a season for club and country which ended in disappointment.
Losing out on a potential Triple Crown to Wales, the home of his regular employers the Llanelli Scarlets, riled the Yorkshire-born back row in March.
So too did the Scarlets' failure to make it out of the Heineken Cup's Pool 3, having been overthrown by eventual champions Toulouse and the Northampton Saints. Munster also got the better of the Easterby-skippered Scarlets in last month's Celtic Cup final, which had the Ireland international admitting his side were "missing that little bit of class", and forecasting that "the summer will be all about recruitment" for the Welsh region.
Easterby will want a strengthened Scarlets by the time the new Anglo-Welsh Cup and Heineken Cup roll around next October - especially with his signature already on a new three-year Stradey Park deal.
But right now, his sole concentration is on the Lions' mission in New Zealand.
At his first press briefing in Auckland, Easterby conceded: "I am not coming here to fill Lawrence's boots - he is a one-off.
"It is a huge blow for him and a real disappointment, but I will hopefully bring something of my own to the tour and make a positive impact when I get the chance."
He added: "I was not expecting it but I was hopeful that if there was an unfortunate case where someone got injured and was out of the tour, that I would be in the frame to come out here.
"The squad has been together for a few weeks now and I have only come in today (Sunday). There is a lot I need to fill my mind with."
Dallaglio, who is due to return home to England in two weeks' time after breaking and dislocating his ankle against the Bay of Plenty, backed Easterby by saying: "He's come out here on the back of a fantastic Six Nations and this is a really good opportunity for Simon."
Dallaglio was ironically a former team mate of Easterby's at North Yorkshire's Ampleforth College.