IMO these disaster extensions bring disaster to folks who were otherwise unaffected.

I can't speak to what Lacerte may or may not do but:

1) If you're planning on filing an extension anyway, do it by the April due date.  Historically you've been unable to efile them (or file them via DirectPay) after the pre-disaster deadline.  The IRS computers are not equipped to understand what you're trying to do.  In most cases in the past if you need to file an extension between 4/15 (or 16, 17, 18 whatever day of the week we're on this year) and the disaster deadline you have to file ON PAPER.  Which then sits in a trailer waiting to be opened until likely long after you've efiled the return and the IRS has assessed penalties.  You can eventually argue your way out of them but be sure to bill your clients way more than they "saved" by holding onto the money for an extra month.

2) If you're not filing an extension, file on time.  Clients can make a tax payment on DirectPay by the disaster extended deadline.  But even then, unless we're talking millions of dollars, the time value of one month is much lower than the stress cost of trying to get someone at the IRS to fix something if it goes wrong.