The 2005 Lions, led by Ireland captain Brian O'Driscoll (pictured above, at Auckland airport), begin their assault down under next Saturday against Bay of Plenty, and follow it with difficult outings against Taranaki and the All-Black backed New Zealand Maori XV.
O'Sullivan said: "Every game we play here in New Zealand we will be tested. That makes a Lions tour unique and if we don't go into every game with that mentality we will get turned over.
"That starts in Rotorua where Bay of Plenty will try and throw the kitchen sink at us.
"We have got to get our heads around that very quickly. That will make us a better team.
"We will get to the Test side knowing all the players have been put through the mill and we know what we are picking from," added the Corkman.
Definitely out of contention for the opening Lions tour side, which is named on Wednesday, are French tied-duo Gareth Thomas and Stephen Jones, so too is England full-back Jason Robinson, who is currently nursing his unwell wife at home, and is likely to miss the squad's first three matches.
Ireland lock Malcolm O'Kelly has made a solid recovery from the abdominal muscle strain that kept him out of last Monday's 25-25 draw with Argentina.
The 30-year-old O'Kelly is expected to be fit for selection for the Bay of Plenty clash, although Scotland's Simon Taylor (hamstring) is a doubt.
Sunday sees the Lions take part in their first "open" training session of the tour at Auckland's North Harbour stadium.