Hi,
I suggest to display "32-bit" or "64-bit" in the caption of Lazarus.
I work with both versions and switch very often and it's difficult to check if I run the correct version for me.
As a workaround and while you wait for the feature to be added to Lazarus, you can use Process Hacker 2 or Process Explorer (both free downloads). In Process Hacker ensure you've selected "Bits" as a column, in Process Explorer, under Process Image, select "Image Type".
That will allow you to quickly check any program's bitness. Both utilities provide a wealth of information about a process which is often useful when debugging.
HTH.
ETA: take what follows with a grain of salt since I have not tested it.
It seems that it would be easy to add the feature you've asked for, yourself. If you open Lazarus.lpi, you'll see "Application.Title := 'Lazarus';". It would seems that simply changing the title to include the bitness would satisfy your request. Simply check what the size of a pointer is and, if 8 then append '64bit' to the title, otherwise append "32bit" (or something along those lines.)