Lately

Amir OghlowShe had done her work lately before he came.

No. Leave out "lately".

Amir OghlowIs it correct to use "lately or recently" in past perfect or past perfect progressive?

Not with "lately" anyway. "recently" seems OK though: They had recently painted the bench, so it was still a little sticky.

CJ

Why did they do it in recent years.
Why had they done it in recent years.

Are they both okay?

Amir OghlowAre they both okay?

"do it" is so very vague that it's hard to judge your sentences. The first one seems wrong; the second one doesn't seem quite so wrong, but it doesn't sound right either.

You need a question mark on both of them, by the way.

CJ

They had worked together when I met them
They had been working together when I met them.

Is there difference?

Amir OghlowThey had worked together when I met them. They had been working together when I met them. Is there a difference?

Yes.

had worked - during some period of time before I met them, but ending some time before I met them
had been working - during some period of ti

I had studied them one year before.
Is it correct?

Amir OghlowI had studied them one year before.Is it correct?

As it stands, it is not correct. Past perfect requires two past actions in the context, but you have no context.

I studied it a year earlier.
I had studied it a year earlier.

Which one is correct?

Amir OghlowWhich one is correct?

Both are correct.

If I want to say "before a year" is it correct?