[AmE - not a teacher]
I can't tell you why, but "lately" to me gives a clue that it's been this way for a while, and up through now, and quite possibly in to the future. "Recently" to me sounds like it has happened only in the immediate past, and may not continue.
1: Why so blue*?
2: I don't know, I've been sad lately.
3: Is it because your dog died recently?
2: I'm sure that's part of it.
*3a : low in spirits : melancholy
Blue - Definition and More from the Free Merriam-Webster Dictionary
Student or Learner