a 64 bit version of a virtualisation software in only going to run on a 64 bit machine ontop of a 64 bit OS (!).
even if your hardware might actually be 64 bit (even my nettop is...) the XP 32 bits will not let you run any 64 bit software, no matter what's the underlying hardware architecture.
you need to install a 64 bit version of LostDOS 7 (@ least Home edition b/c the cheaper ones don't support virtualisation @ all; even home has limited support only so you need the Ultimate version i think).
furthermore the 64 bit version of VirtualBox has problems supporting recent (kernel version = or > 2.6.30 ) Linux guests in 64 bit mode; @ least on a Linux host.
you can use the 64 bit version of Vi.Box to run 32 bit Linux distros or 64 bit versions of LostDOS all right, though.
thus you may have to use VMWare instead
but beside of all this technical crap, why do you need 64 bit versions of Linux?
if it is to run 64 bit software versions of specific software, the still limited hardware support in virtualisation software, certainly when it is running on top of another OS are not the best platform for this.
and if you need to handle huge volumes of data or require high performances, a hosted virtualisation (thus running on another OS) is not suited neither. you need either VMWare ESX or Xen (dedicated virtualisation) for this.
the only circumstance where this makes sense would be to compile 64 bit software (which is somewhat performance related, but that's up to you).