Something that happened lately occurred very recently. If you've spotted a fox every day for the last week, you might say, "I've seen so many foxes lately!"
If your friend says, "I've been really stressed out lately," she means she's been overworked and tense for the past few days, weeks, or possibly months. Lately is an adverb that covers the immediate past, a period of time that wasn't too long ago. A more old-fashioned way to say lately is "of late." Though this word has had its current meaning since the fifteenth century, it originally meant "slow or sluggish."
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