22-year-old Lavery, who has played for the Northern Ireland U21s, gets his chance after an impressive season for the Owls.
Ross County forward Liam Boyce who has won four caps and was on last summer's South American tour, recently scored the winner against Hamilton five minutes from the end to secure his club's Scottish Premiership safety.
Michael O'Neill's Northern Ireland side will face Qatar on 31 May in Crewe before the Euro 2016 Qualifier against Romania in Belfast clash on the 13 June.
Cheltenham goalkeeper Trevor Carson returns to the 28-player squad in place of Alan Mannus who is getting married.
Goalkeepers: Roy Carroll (Notts County), Michael McGovern (Hamilton Academicals), Trevor Carson (Cheltenham Town)
Defenders: Aaron Hughes (Unattached), Chris Baird, Gareth McAuley (both West Bromwich Albion), Jonny Evans (Manchester United), Craig Cathcart (Watford), Shane Ferguson (Newcastle United), Daniel Lafferty (Burnley), Conor McLaughlin (Fleetwood Town), Luke McCullough (Doncaster Rovers), Paddy McNair (Manchester United)
Midfielders: Steve Davis (Southampton), Chris Brunt (West Bromwich Albion), Corry Evans (Blackburn Rovers), Oliver Norwood (Reading), Pat McCourt (Unattached), Ben Reeves (MK Dons), Stuart Dallas (Brentford)
Forwards: Kyle Lafferty (Norwich City), Josh Magennis (Kilmarnock), Billy McKay (Wigan Athletic), Will Grigg (Brentford), Niall McGinn (Aberdeen), Jamie Ward (Unattached), Liam Boyce (Ross County), Caolan Lavery (Sheffield Wednesday)
Caolan Lavery in action in the UEFA Under 21 Championship Qualifier against Italy.