I did some testing in practice mode and it looks like it's 200 health.
Used fire to get the gun down to almost no health
Hit it with a spanner 4 times:
The fifth spanner hit fully repaired the gun:
Since each spanner hit repairs 40 damage, I repaired 200 damage total, which was enough to fully repair the gun. Therefore, light gun health cannot be 250.
Visually, each square looks like it represents 40 health. 40*5=200.