Through the Secondary Nature of Immune Influence, Gappu could latch onto a Slump Lizard's body once his claws dig into the latter. Following that, he would be able to influence the Slump Lizard's behaviour and decision-making.
If his strength is sufficient, he'll be able to influence the Slump Lizard and control it like a mount, able to ride it. The degree of influence is entirely dependent on the target's strength.
Influencing Iron Grade Pranic Beasts was possible, with Beginner Iron Grade and Intermediate Iron Grade Pranic Beasts being the easiest to influence. The success rate for Advanced Iron Grade and Expert Iron Grade Pranic Beasts would be vastly lower.
It was pretty much impossible to influence a Silver Grade Pranic Beast. But, Immune Influence was special, in that Inala took inspiration from Slump Lizards in their ability to stack Natures on a target.