According to Raymond murphy and the Cambridge dictionary and Raymond Murphy, Lately is used in the sense of recently and till now or upto now or just now.
I haven't been feeling well lately
I haven't seen him lately
But In Collins dictionary lately is used in simple last, past perfect and past perfect continuous too.
When different dictionaries say differently and use lately in different tenses, it is difficult to say what the correct use of lately is.
So I think:
I had a letter from my friend lately
I had a strange experience lately is not wrong but may be unusual.
I have had a letter from my friend lately is usual.
Here are the two links