Question

The lightning flashed, and the thunder
rumbled immediately after.

Answer 1

Here are a few clearer or more polished ways to phrase that idea, with brief notes:

- Lightning flashed, and thunder rumbled immediately afterward.
(Concise; “afterward” is slightly more formal than “after.”)

- Lightning flashed; thunder rumbled right behind it.
(Stronger rhythm; semicolon links the two independent clauses.)

- Lightning flashed, and immediately after came the thunder.
(More emphatic placement of timing.)

- Lightning flashed, followed immediately by thunder.
(More compact, slightly more literary.)

- The lightning flashed, and the thunder followed.
(Simple and classical.)

Note: The sequence is correct physically — we see lightning before we hear thunder because light travels far faster than sound. Grammatically, a comma before “and” is appropriate when joining two independent clauses (as in your original sentence).