Lavery went close for Wednesday early on, but hit his shot wide after Chris Maguire had put him through.
It was Lavery who then gave the home side the lead just before half time, scoring from close range after Lewis Buxton's cross.
Lloyd Isgrove almost doubled Wednesday's lead immediately after the break, but saw two attempts saved within a minute from Henderson.
Gudmundsson equalised for Charlton with 15 minutes remaining, pouncing on the rebound after Eagles's initial attempt was saved.
Neither side could find a winner, with the draw leaving Wednesday in 13th place and Charlton 11th.