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"Whiteacre to I for life, then to K if she lives to be 25, otherwise to L."

I understand that K is valid because she must get it either within 21 years after I's death or during her (K) own lifetime. And I understand that L is valid because if she does get it, she must get it within 21 years of K's death.

What I don't understand is why you can't base L's valid taking on the fact that L is a measuring life, and therefore, if she does take, its valid because she will take during her own lifetime.

Any help will be greatly appreciated.

I'm unsure about this, but: is it necessary to specify "to L and her heirs"? In other words, while L is a life in being at the time of the grant, she may still receive the interest even if she's dead. It will just pass to her devisees or heirs.

Probably too late but since to L implies L's heirs get an interest, and they may not be alive or ascertainable those heirs cant be measuring lives. If I and L die and then K makes it to 23 then dies, then there will be an executory interest that is activated more than 21 years after the death of all of the lives in being at the time of the grant. Thus it violates the rules against perpetuity.

I know this is probably too late to help since this was most likely a spring semester Property question, but...
This isn't an RAP issue. The issue here is the ability to determine who takes with certainty at the time the interest becomes possessory. When I dies, we know that it's intended that the estate pass to either K or L in fee simple. However, if I dies while K is 1) alive, but 2) not yet 25 years old, we have no idea whether the condition precedent to K's vesting will be satisfied or not, so we don't know whether it's K or L who takes. That's a no-no.