Learn Spanish (Latin America): Como el contador mienta, ¿cómo vamos a justificar la cuenta? - If the accountant lies, how are we going to justify the bill?

Because the sentence starts with Como used as a conditional warning. When como means "if" and sets up a threat or a strong warning about a negative outcome, it must be followed by the present subjunctive.

Why use Como for "If" instead of the usual word, Si?

You could definitely use Si here, but starting a sentence with Como plus the subjunctive adds a specific tone of warning or dread. It emphasizes that the accountant lying is a bad scenario that you really want to avoid. Note that if you used Si, you would have to use the normal present indicative verb miente.

Why does the second cómo have an accent mark while the first Como does not?

The second cómo is a question word meaning "how," and all question words in Spanish require a written accent mark. The first Como is a conjunction here meaning "if," so it does not take an accent.

Is there a connection between the words contador and cuenta?

Yes, they share the same root from the verb contar (to count). A contador is an accountant (someone who counts), and cuenta means a bill, check, or account. In this context, la cuenta refers to the bill or financial record they are going to have trouble justifying.