No, your observation is not quite correct.
"Recently" is defined in Cambridge as "not long ago, or at a time that started not long ago". So, it can be used for single events or ongoing situations. For example:
- I recently visited my parents (a one-off event)
- I've been reading more, recently (ongoing)
"Lately" is only used for recent, ongoing matters. It often is interchangeable with 'recently', but we tend to use it for things for which we may not refer to a specific starting point, such as talking about how we feel (eg "I've been feeling unwell, lately") rather than things that occured at specific times. You are perhaps less likely to hear "I've been visiting my parents lately", but you may hear "I've been visiting my parents more, lately", because the increase in frequency is not a specific point in time.