>>Is there a command I can run from these systems that will allow
installation to hard drive?
As Steve suggested there are options to install directly from the boot menu.
When you get to the boot menu you will see what is there.
>>I find nothing on menus or desktop, and the
package 'debian-installer' seems not to be in the repository.
Before this can be answered properly what "live" system are you using? Are you using the official system based on live-wrapper or are you using the, now unofficial, system based on live-build?
Live Build had an option in the menu of the running live system, I am not sure about live-wrapper though.