This is one that came up in something I was editing a few days ago. And, I admit, one that I had to check in the dictionary. I was pretty sure the writer wanted unmeasurable (I was right), and I wasn’t sure that immeasurable was a word (I learned something, notably that SpellChecker doesn’t think it’s a word, which is why we still use dictionaries!).
Unmeasurable means, specifically not able to be measured objectively. We use this one in the literal sense: “the immense lizard was unmeasurable with the tiny ruler in the standard lizard measuring kit”; “the sea trench in which the angler fish lived was of an unmeasurable depth”.
Immeasurable means, a bit less specifically, I suppose, too large, extensive or extreme to measure. We should reserve this one for the more figurative sense (otherwise there’s no point in having two different words, is there, and where would THAT leave us?): ” the immeasurable mercy of their god”; “he had immeasurable ambition”.
“I experienced immeasurable relief when I discovered that the width of the lake, filling and evaporating as it did, was actually unmeasurable.”