Not an expert on this. Will post my opinions!

mehaksal wrote:Choose the sentence with properly used idiom (emphasized with boldface). Please note that a wrong answer choice may be grammatically correct.

1. What these scores tell us is that rigor is lacking in some schools.
//rigor is not lacking...but schools are lacking

2. What these scores tell us is that some schools lack of rigor.
//wrong - schools are lacking in rigor

3. What these scores tell us is that there's a lack of rigor in some schools.

//correct

sorry..I didn't get ur reply...u mean 3rd??

mehaksal wrote:Choose the sentence with properly used idiom (emphasized with boldface). Please note that a wrong answer choice may be grammatically correct.

1. What these scores tell us is that rigor is lacking in some schools.
2. What these scores tell us is that some schools lack of rigor.
3. What these scores tell us is that there's a lack of rigor in some schools.

As far as idioms is concerned, I do not think that this is the issue here. The usage of the verbs is the main problem -


1 - correct.
2 - incorrect : "that phrase" lacks a main finite verb..or in other way we cant use a "of" phrase in this way.
3 - correct.

"lack of" is generally used when "lack" is a noun, lack of confidence...
and "lack in" is generally used to signify adverb of place when "lack" is a main verb, as in the example 1.


Hope this helps !!