How have you been doing lately? Have you been studying your English? If you haven't been studying English lately, perhaps you've been doing other things. You could say, "I've been working a lot lately." Or, I've been doing a lot of gardening." Or, I've been helping my brother rebuild his house after the tornado tore his roof off."
As for your teacher, I've been doing a lot of things lately. Right now I'm enjoying a vacation from my regular teaching assignment. School starts up again in two weeks, so I have a little time off to do things that interest me. So, if someone asked me the same question I'm asking you, I'd have to say....
I've been riding my bike around town a lot lately.
I've been cleaning my basement. (It's really a mess.*)
I've been spending time with my kids.
I've been working on my website.
I've been fixing my house. (It's old and needs repairs.)
I've been planning on taking a trip to Chicago.
I've been taking pictures with my camera. The pictures are for my website. �