I was sued by an out of State attorney for legal fees. I appeared by telephone for the hearing, but being that I am not an attorney and had no funds to hire one, I lost the case for not knowing the correct legal procedure of filing all answers necessary.

I own no property or funds to pay this debt and live on Social Security income only, which is deposited into a bank account every month.

What can I do if the attorney attaches these funds?

Social security is only allowed to be garnished by few things such as money owed the government and student loans.
I would call social security and ask what is the best way to handle this and what rights you have against them doing this. Also make the bank aware that the money is social security money and therefore except from most garnishments.