Is there any other method other using prior data to try and predict how many slots will potentially be open? Not an exact science, but I guess somewhat helpful in an area where there is little to go on.

Why do people compare past results as if they know how many PK3ers are entering for the following year?

Those PK3ers are now PK4 students.

LAMB isn't in the common lottery; therefore you have an outside option.

None of the charter schools will know how many non-sibling or open slots they will have. But it's not that difficult to know how many total slots each school will likely have (number of classes for PK3 or PK4 times # of kids per class).

For example:
CMI: 3 classes of 17 kids
ITS: 2 classes of 21-22 kids
MV: 4 (?) classes of XX kids
YY: 4 (?) classes of XX kids
Stokes: 2 classes of XX kids

The Montessoris are a bit trickier because it depends on how they balance their primary classes (mixed grade) and how many kids are in each (typically close to 30).

Etc.