Does anyone know what time in the US does TLG release new sets on release dates?  For example, the sets due to release on May 1st, will those be available at 12:01am Eastern Time in the US?  Or is it random?

You mean if you wanted to purchase a new set from LEGO's website which time zone do they adhere to generally? I've never really thought about it but now I'm curious.

Time and timezone, really.  If I recall things correctly, when the Elsa's Castle was released, I tried right after midnight and again just after 1 am Central Time, but it was still not available to buy.  Later in the morning, like around 7 am, it showed available to buy, but it said it would be delayed delivery.  So, I'm guessing that the release happens at like 5 am so that it's truly the same date for all timezones in the US.  

The new Simpsons CMF became available online at LEGO Shop at Home.  It was just slightly after midnight, Central Time in the US.  

I wonder if this is dependent on the timezone you are in somehow.