Hmmm ... it might fit.
Doing a little math ...
Let C = 11.25" the radius of a 22.5" diameter
Let A = 6.5" half the width of the rack's 13" width
Using Pythagorean's therorm A^2 + B^2 = C^2 and solving for B ... = 9.19"
Half the width of the rack's 18" length = 9"
9" < 9.18"
Therefore, it will fit ... barely.
BUT ... not sure about the heigth cuz I don't have the curvature of the 22.5" lid.
But, assuming it's a circle, using the same formula, the height of the lid at 9" should be 6.75" so it just should fit.
A picture is worth a thousand words ...
And you thought you'd never see this stuff again after High School.
Update: Oops, discovered a typo in my math.