From: Lingoda Class Report (Jessica), Cambridge Dictionary
There's a great page here on the Cambridge dictionary site with some more info on when to use late, when to use lately and when it can be swapped with recently! https://dictionary.cambridge.org/grammar/british-grammar/late-or-lately
Late: Late as an adverb means ‘not on time’:
Well, I couldn’t find my classroom, so I got to the classroom a bit late and then I had to sing a song in front of the other students!
Lately: Lately is used for REPEATED events. Something that is recurring often. We use lately for states or for repeated events, mostly with the present perfect:
She says she’s been feeling tired lately. I think she’s working too much.
You asked me if you could interchange 'recently' and 'shortly,' and I said no. Here is why:
Recently (adverb) meaning - at a recent time; not long ago.
- Recently means something just happened. "I recently started studying astro-physics!"
Since the sentence suggests that Jane and Amber have arrived late to the party this one time, we use recently.
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Shortly (adverb) meaning - in a short time; soon.
- Shortly means something is about to happen. "I will start studying astro-physics shortly."