Learn English – His greatness – “lies” or “lay”

So, in the following extract, students are supposed to fill the correct form of the word (given in the parenthesis) in the blank beside it. The first one (0) has been given as am convinced. Here's the passage:

From ICSE board paper Page 5 Question 4,

I (0) ____ (convince) that my father (1) ____ (remember) by all those who value integrity. He (2) ____ (be) a man of learning and also saw to it that he (3) ____ (teach) his pupils with passion and patience. He, at times (4) ____ (use) to lose his temper, but that was because he always (5) ____ (want) his pupils to learn and learn well. As a person, he was honest and simple. His greatness (6) ___ (lie) in the fact that he (7) ____ (have) a pure heart, devoid of malice. Such a man is always valued and (8) ____ (be) very rare to find.

Here are my answers:

1. is remembered
2. was
3. taught
4. used
5. wanted
6. lies
7. had
8. is

Problem: All my answers except point 6 were marked correct. So the passage reads:

I am convinced that my father is remembered by all those who value integrity. He was a man of learning and also saw to it that he taught his pupils with passion and patience. He, at times used to lose his temper, but that was because he always wanted his pupils to learn and learn well. As a person, he was honest and simple. His greatness (6) ___ (lie) in the fact that he had a pure heart, devoid of malice. Such a man is always valued and is very rare to find.

Question: Is my teacher correct when she says that the point 6 should be "lay" not "lies"? In my opinion, even though the man is dead, his greatness is present (and that's the reason why he is remembered (point 1)). And since 'greatness' is present, the verb lie should be written as lies in point 6.

What's the correct answer for point 6 and why?

UPDATE: (to answers by VarunKN and miqdadamirali) While it is true that the sentence and most of the passage are in past tense, but the fact is that verbs must agree with their subject, and so that the verb lie should agree with its subject greatness. So, since greatness is still present and exists, therefore the verb should be written as lies

UPDATE 2: Thank you all! I am finally convinced that the verb should be lay. Here are some points to note:

1. You used 'had' as you answer for (7). Now since that is in the past, you should've used 'lay' to maintain the tense of the sentence. And to start with, the sentence is already in the past tense with the inclusion of 'was'. (Varun KN)
2. His greatness lay in things that only held while he was alive. He is no longer alive and therefore no longer great. That is to say that he is no longer honest and simple with a pure heart devoid of malice, so he is no longer great. (Brythan)
3. Another point: even in cases where someone is still great, it is controvertible that he was great while alive. So lay is always correct. In some circumstances, he may still be great. In this case, the context is to talk about his characteristics while alive. His greatness in life is clearly past tense. (Brythan)
4. It is exceptionally hard to write a passage in which every blank or every choice will have one correct answer. (Go Ducks)