I'm not sure if you can convert a lease into a purchase, for which you would still have to purchase the equipment (it's not rent to own), or whether you'd have to terminate your current service, then enter into a new agreement, but with a purchase instead of a lease.
Judging by $300 non returned equipment fee that is assessed if the equipment is not returned within a set amount of time after service termination (30 days?), it would likely still be at least that amount to purchase the equipment on the current account, if that's even an option.
It would be better to ask what your options are in the "My Account and Billing" section.
But yes, like maratsade confirmed, using HughesNet equipment is a requirement, as it alluded to in the agreement.