The scrum-half played a key role in the tourists 22-17 victory over South Africa in the first Test in Cape Town and is set for a second Test cap off the bench if called upon by Warren Gatland.
Price played 65-minutes on Saturday and put out a strong account of himself kicking and passing well.
Price is one of five Scots named by Gatland and his coaching team, with Duhan van der Merwe, Rory Sutherland, Chris Harris and, former Warrior, Stuart Hogg joining Price in the matchday 23.
British & Irish Lions
15 Stuart Hogg (Exeter Chiefs, Scotland)
14 Anthony Watson (Bath Rugby, England)
13 Chris Harris (Gloucester Rugby, Scotland)
12 Robbie Henshaw (Leinster Rugby, Ireland)
11 Duhan van der Merwe (Worcester Warriors, Scotland)
10 Dan Biggar (Northampton Saints, Wales)
9 Conor Murray (Munster Rugby, Ireland)
1 Mako Vunipola (Saracens, England)
2 Luke Cowan-Dickie (Exeter Chiefs, England)
3 Tadhg Furlong (Leinster Rugby, Ireland)
4 Maro Itoje (Saracens, England)
5 Alun Wyn Jones - captain (Ospreys, Wales)
6 Courtney Lawes (Northampton Saints, England)
7 Tom Curry (Sale Sharks, England)
8 Jack Conan (Leinster Rugby, Ireland)
Substitutes
16 Ken Owens (Scarlets, Wales)
17 Rory Sutherland (Worcester Warriors, Scotland)
18 Kyle Sinckler (Bristol Bears, England)
19 Tadhg Beirne (Munster Rugby, Ireland)
20 Taulupe Faletau (Bath Rugby, Wales)
21 Ali Price (Glasgow Warriors, Scotland)
22 Owen Farrell (Saracens, England)
23 Elliot Daly (Saracens, England)