Ah, this looks like him, only one of that name listed for warwickshire in those years -
Full name: John Lynes
Born: 6th June 1872, Coleshill, Warwickshire, England
Batting: Right-hand batsman
Bowling: Right-arm fast-medium
Teams: Warwickshire (Main FC: 1897-1905); All teams
Lists of matches and more detailed statistics
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First-Class Career Batting and Fielding (1897-1905)
M I NO Runs HS Ave 100 50 Ct
Overall 8 8 0 79 26 9.87 0 0 6
First-Class Career Bowling (1898-1905)
Balls Mdns Runs Wkts BB Ave 5wI 10wM SRate Econ
Overall 933 26 576 15 3-54 38.40 0 0 62.20 3.70
This page was created by the CricketArchive Oracles
So he made eight First Team appearances according to that.