UPDATE ---
I ran file -s on my executable, and found this:
Test1: ELF 64-bit LSB executable, x86-64, version 1 (SYSV), statically linked, for GNU/Linux 2.4.0, stripped
So, it already is a 64 bit executable. (The default Lazarus installation on 64-bit Linux Mint must be set to that.)
And, I still have the problem. Any other ideas?