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Is your computer using wireless or wired connection?
It is possible to boot a VirtualBox guest from a physical USB drive but you need to create a vmdk machine disk file. Did you create the vmdk disk file or did you select the ISO file when you booted the virtual machine? VirtualBox uses a well supported Intel wired network adapter by default and lubuntu should of been able to recognize the "virtual" hardware.
Otherwise did you boot the computer from the USB drive instead of Windows. In this case this will be a dual boot system and it is possible lubuntu did not recognize the network adapter. If using wireless then from the following link it appears to be an Intel dual band wireless ac-3168 and the driver is probably not installed by default. If you want to run linux as a virtual machine I hoped you have canceled the installation.
https://h30434.www3.hp.com/t5/Busine...0/td-p/6426344
I installed lubuntu x86 version successfully as a VirtualBox guest and networking hardware was recognized. Why are you trying to install a 32 versus 64 bit version?