is it legal to purchase 2 different properties simultaneously with 2 different lenders/banks using 1 credit applicant?

A double-close may not be legal if it's done without the disclosure to both lenders. This kind of closing happens a lot with investors. There have been instances where an investor would close 3-7 properties in one day at one closing. Lenders aren't happy when they're put in this sticky situation. They may fear that it's an investment where there may be a higher chance of default. Additionally, it may appear unethical and unlawful if full disclosure was not made. I would consult with a RE Attorney for more clarification.