Run-on sentences:

1a. Both Lisa and Alan enjoy photography; both have won prestigious awards.
1b. Both Lisa and Alan enjoy photography, both have won prestigious awards.
Which one is correct and why?

Do you see two separate sentences?

Both Lisa and Alan enjoy photography.
Both have won prestigious awards.

To separate two complete sentences (or independent clauses), you need a semicolon or a period between them.

yes i do see 2 complete sentences, so then i would use a semicolon between them since we are discussing semicolons. thank you

Yes. 1a. is correct.

The correct sentence is 1a: "Both Lisa and Alan enjoy photography; both have won prestigious awards." This sentence is correctly punctuated because it uses a semicolon to separate two related independent clauses.

A run-on sentence occurs when two or more independent clauses (complete thoughts) are joined together without proper punctuation or conjunction. In run-on sentences, the clauses are incorrectly merged, making the sentence unclear or confusing to read.

In 1b, a comma is used instead of a semicolon to separate the clauses, resulting in a run-on sentence. Commas are generally used to separate items in a list or to separate dependent clauses from independent clauses. To correctly join two independent clauses without a coordinating conjunction (such as "and" or "but"), you should use a semicolon or a period.

So, the semicolon in sentence 1a correctly separates the independent clauses, making it grammatically correct and avoiding a run-on sentence.