"lately occurred" is correct and can be used in written English.
You can use it to refer to something that has recently happened. For example, "The devastating earthquake that lately occurred claimed many lives."
Americans, he says, are "trying to figure out how to be happy", but lately "it occurred to me that I have some of my father's depressive temperament.
"Lately it occurs to me What a long, strange trip it's been" -The Grateful Dead.
There is also the practical matter of a dedicated tax and benefit structure avoiding the yearly budget fights that have lately been occurring at more frequent increments.
My entire career has been evaluating applicants on their professional experience, but lately it occurs to me that huge chunks of skills and talents are missing for parents who also identify as the Default Parent... you know, the ones responsible for the daily logistical and emotional needs of the children.
Lance had his theories, but lately it had occurred to Kirsten that he was conducting his life with folklore.
The Council of Europe delegation "might have seen positive changes that have occurred lately had they really wanted to see them," the statement added.
Reagan lumped together all of the various acts of terrorism that have occurred lately, insisting that they were all of a piece.
And though I was relieved to know that I loved her with the exact same level of bone-crushing fervor I loved my son, lately it has occurred to me that the love is still different.
Because the proposed device was constructed of trench-type electrodes, the electric field moved toward trench-oxide layer, and punch through breakdown of LTEIGBT is occurred, lately.
Some strikes which have occurred lately indicate that the employees were simply tired of working without a break and that they resorted to a strike as the only means of obtaining a good rest or a fling at recreation.
