Final Answer?

In Hungarian orthography, ‘ly’ is a digraph (two letters treated as one) denoting a sound that has been lost from the standard dialect but still existed in some dialects up to the early 20th century — i.e., just long enough to screw up modern spelling rules. The sound is basically a palatalized L; people who don’t have this sound in their “arsenal” generally hear it as a consonantal /y/ as in “yellow,” but in some contexts, it can sound like a plain /L/ as in “long.” The č/cs (/ch/ like in “church”) sound in Ilčik/Ilycsik would naturally have caused palatalization of the preceding /L/; the Slovak spelling doesn’t mark this, but the Hungarian one does. ~~~~~ The other thing to consider or keep in mind is that surname spelling was variable right up into the twentieth century. In a society where illiteracy was normal, it was only the sound that mattered. There are countless examples of families who didn’t agree on a single spelling, with brothers or cousins using and passing down different versions. This is true even for people who stayed where they were born; for immigrants dropped into yet another language/spelling context, relatives spelling their names the same is the exception.