Punctuation

If you have a choice, you should make it into two sentences.
"...of the test. Consequently,..."
I am not sure about the semicolon.

Use a comma instead of a semicolon, include "and" before "consequently," and remove the comma.

Lora was late for beginning of the test, and consequently she failed to complete it on time.

"Lora was late for the beginning of the test. Consequently, she failed to complete it on time."

or

"Lora missed the start of the test. As a result, she was unable to complete it."

or

"Lora missed the test's commencement. Due to this, she wasn't able to complete it."

or

"As Lora missed the test's beginning, she wasn't able to complete it."

Correct.

A semi colon can be used in place of a full stop in cases where two sentences are more intimately linked than normal.

A sentence makes sense on its own, Consequently she failed to complete it on time, does not make sense on its own.