I'm going to go ahead and say that Lillian can't take the elements from one's summoning. For example, if Myth started charging his gauntlets with lightning, and they, as usual, began glowing electric-blue and electricity began crackling along his gloves and lower arms, Lillian wouldn't be able to take it. However, if Lillian were paying enough attention and was ready for the moment he would release, then Lillian could take it and enhance it and redirect it. IF she timed it right. It's immediate, instant, and that means you have to get the timing perfect, or you'll miss your chance at redirecting and recharging it.

A fireball or icebolt moves a great deal slower, so you'd obviously have better luck controlling them.