There are many animals that have behaviors or characteristics to make themselves appear larger than they are as a defense mechanism, such as butterflies have large eye patterns on their wings.
Are there any animals that do the opposite? That attempt to appear smaller in order to lure their prey closer?
I'm more interested in physical characteristics but behavior that does this, also counts.
In order to answer your question, two things must be demonstrated: First, we must demonstrate that the prey animal has perceived the predator. Second, we must demonstrate that the prey animal believes that it has perceived a small animal (which poses no threat).
There are several ways that a predator might achieve these outcomes. The first way is to present a small part of its' body as an independent animal, and the rest of its body as something innocuous, like a rock. There are many examples of this type of deception: you've already identified anglerfish lures. My personal favourites are frogfishes. Several other examples are discussed in the Wiki on Aggressive Mimicry.
Another way is to present the whole body in a way that makes it appear small, for instance by presenting a silhouette with a small apparent area to the prey. This has long been thought to be part of the foraging strategy of some ambush predators which have bodies with a small cross-section, such as pike and dories.
In addition to visual deceptions, some predators may use other signals to be perceived as animals that are smaller than themselves. Atkinson (1997) suggests that predatory Northern Shrikes impersonate the songs of smaller Passerine birds in order to lure them into striking range. This behaviour would also qualify as a predator attempting to be perceived as something smaller than it really is in order to gain prey.
This kind of deception can happen at various levels. Mimicry (which you already mentioned), Camouflage, distractions, deceptions, display behaviors. These are not just for predation or avoiding predator but also for reproduction and avoid conflicts. There are many examples of this kind of behavior, I know few of them. All are not exactly reduction in size but something similar to lure prey.
