Correct: Liz continued pushing dirt down around the seedlings, oblivious to the threat at her front gate.
NOTE: If you're a person who doesn't use any commas unless absolutely necessary, you can sometimes omit this comma. However, if there's any possibility that your reader will misunderstand, it's best to follow the rule and include it.
Want more punctuation tips?
Avoiding Incorrect Punctuation Pt 1: Commas Save Lives; the Vocative Comma