I downloaded what I thought would be the 64-bit version of Lazarus:

Although it loads the 32-bit assembly:

And after installing the IDE 32-bit:

And it builds 32 bit binaries:

Changing targeting options on win64, win64, win64:

It gives an error that Lazarus does not support the 64-bit version:

Reading the somewhat outdated Cross-compiling Wiki page gives instructions on how to make Lazarus 64-bit work on 64-bit machines:
From win32 to win64
If you compile the ffc branch 2.1.1 or more, you can simply do:
$ make all OS_TARGET=win64 CPU_TARGET=x86_64
and then
$ make crossinstall OS_TARGET=win64 CPU_TARGET=x86_64
which, if you follow, just gives several thousand errors:

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