Anything Wrong in These Sentences - Lack of Variety

We took a visa exam at university today. The lecturer wanted us to find out the mistakes in some sentences. I was unable to be sure in some of the sentences; for instance, below are two of them:

1- That course book is lack of variety.

In the above sentence, I first thiought there was some mistake in "lack", and so I did in the exam, but after a little bit search, I see that there is nothing wrong in "lack" (at least I found it so )

If the above sentence were "It lacks in variety", would it be correct, or should it have been "It lacks of variety", which, when I googled, saw that structure is rarely used ( and if it is correct). Or else, all this is not true for the above sentence, and is the problematic area of the sentence "variety". Lastly I wonder if there is no mistake at all.


2- Ask your friend what she is doing this evening

This is one of the sentences, too. I believe there is nothing wrong in this sentence. Do you agree, Mr/Ms Native Speakers and Experts?

Thank you all in advance