What is the deadline to file an amended return (1040x)?

The deadline for amending a return is three years from the date that the original return was filed.

Also note, filing an amended return will extend the statute of limitations for that tax year to three years after the date that the last amendment was filed. In other words, your return may be audited for up to three years after you file the amended return.

If divorcees were to amend a tax return from when they were married would the DUE back taxes be applied solely to the one Ex-spouse or still be applied to both since they were still jointly married at the time the taxes were applied?

Both would be liable. A joint return makes both parties equally liable. There are some opportunities for "Innocent Spouse" rules, but they are usually only used in criminal cases.

I did not file my taxes last year simply due to laziness. I owed about $130 to them. Can you advise me on what the implications are? Plus, what will I now owe to IRS and what are my options?

You will owe them interest from April 15 of last year plus a penalty for failure to file which will probably be the minimum of $100. All told it will probably be around $260 now.