However, the LVC (low voltage cutoff) is higher in a controller designed for SLA bricks. SLAs cannot be depleted as much as Lithium batteries without suffering permanent damage.
-Using your SLA controller with new Lithium batteries will not cause any harm. Your range would suffer a bit, due to the LVC not being optomized for Li batts.
-Maybe its best to try the Li batteries with your SLA controller and see how it goes. You can buy a new controller later if desired.