The Auckland franchise were able to put together the move of the match to score the game-winning try in the final 10 minutes though, two superb offloads unleashing West to go over.
They will continue their tour with a match against Super Rugby side Crusaders on Saturday, following yesterday's defeat to the Blues.
Lions team: Hogg, North, Davies; Te'o, Williams, Farrell, Murray; Vunipola, George, Furlong, Jones (capt), Kruis, O'Mahony, O'Brien, Faletau.
At least two thirds of this Lions XV appear likely to start the first Test and they will need to raise their game to cope with a strong-looking Crusaders side containing numerous All Blacks.
The Crusaders have picked nine All Blacks in their matchday 23 to face the Lions in Christchurch on Saturday.
The Lions has only once enjoyed a series victory over New Zealand, back in 1971, and this crop of players will be underdogs playing against an All Blacks side on a record run of 45 unbeaten home games.
The Crusaders front five, led by skipper Sam Whitelock, are all full All Blacks and set the platform from which an enterprising back division can play.
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He is, according to Lions head coach Warren Gatland, "one of the top players in northern hemisphere rugby". It'll give us great preparation heading into the All Blacks.
In their favour perhaps is the fact that they are starting halfback Conor Murray, an Irishman who can hold claim to being one of the best No9s in the world, and Englishman Owen Farrell, a talented operator and presumably their starting No10 for the first test on June 24.
Gatland's critics say his teams play "Warrenball", using big centres who burst into opposition territory and draw in defenders to create space for the backs.
"Hugely disappointed, we came here to build on Saturday's performance, we got a good victory up in Whangarei, and we came here to get another win but unfortunately we've got a defeat", he said.
Meanwhile, all three of the Barrett brothers - lock Scott, fly-half Beauden and outside back Jordie - have been named in the New Zealand squad for the Test series. "There are plenty of good players in this squad and to see how they go about everything they do is a brilliant way of learning for everybody". "We also understand that with the potential test match focus of it, we have to adapt", Robertson said. "The way they fought hard to the end to get that result we needed and wanted".
Replacements: K Owens (Wales), J McGrath (Ireland), D Cole (England), M Itoje (England), CJ Stander (Ireland), R Webb (Wales), J Sexton (Ireland), A Watson (England).
Tune into talkSPORT from 8:30am on Saturday morning for LIVE and EXCLUSIVE commentary of The British and Irish Lions v Crusaders! "Anyone who knows anything about rugby, he's a world class seven", Robertson.