Lindsay suffered a five-inch gash in his thigh during the Eagles’ win over Featherstone Rovers.
The injury has been blamed on a U2 concert which was staged at the Don Valley Stadium leaving the pitch in an almost-unplayable condition.
“Brendon’s chances are very slim, I doubt he will make it,” said Aston.
“I’m not happy about what’s happened. This was an injury sustained not as a result of the game but because of the state of the field.”
“Brendon’s our ‘go-to player’. He controls a game by his authority – we need him for a game like this.”
The state of the pitch has also drawn complaints from Huddersfield Town and Rochdale AFC who have played Rotherham United there in recent weeks.
Barrow need only a point from this game to claim the Championship League Leaders’ Trophy after a difficult week in which caretaker coach Steve Deakin was sacked followed by a home defeat to Gateshead Thunder.
If Sheffield win they guarantee a third-placed finish which gives them a home tie in the play-offs.