Don’t you have another constraint?  lp < p

Use DesignModeler and create input parameters: s, lp, n, p and e.

Sketch a rectangle. Apply a constraint of equal lengths to force it to be a square. Add a horizontal dimension to size the square. After dimensioning, go to the Parameter/Dimension Assignments tab of the Parameter Editor and type in the expression that constrains the length to be equal to your equation.

Turn that sketch into a surface or solid.  Create another sketch, use the equal constraint on two edges, and dimension the length of the patch and the offsets for the s parameter. Extrude that into a solid using Add Frozen so it is a separate Body. Use the Pattern menu to copy that solid according to the n and p parameters. Note that in DesignModeler, the n stands for the number of copies of the original, so when n = 4, you get a total of 5 x 5 patches.

Now you have a completely parametric model that obeys the constraint equations, but you have to be aware to keep lp < p.