lie : stative?

Yes, it is. You can read Wikipedia about it: 'Stative verb'.

But what is confusing is that the progressive tenses of 'lie' are frequent.

Yes, it is. Because people often use it in Progressive Tenses, like: 'He is lying on his sofa'. and soo oooon

Why do people use progressive tenses of 'lie' instead of non-progressive tenses?

Thanks. Then, when it comes to the 'past progressive'?

I believe that there are two variants:
1) He was lying on his sofa from 5 to 6. (Cause you have from 5 to 6)
2) He was lying on his sofa. (Here you emphasize the duration: He was lying and even didn't stand up)

3) He was lying on his sofa while she was watching TV (you have 'while')