It's easier to get stronger relative to the elder asshole NPCs in fucking Vampire than Exalted. The high-essence shit was poorly planned to start with and has never been good.
Somewhat better in 3e, for what it's worth.
"Shoggoth stuff" really doesn't suit the predatory Lunar at all. It presents a whole catalog of its own themes that do not enhance Lunar themes and in many cases contradict them. A proper exploration goes a lot deeper than merely stapling on a few gribbly bits and effects, implying a fundamental alienness of not only form but of mind that is wholly unsuitable for Lunars. Loki doesn't screw you over for inscrutable purposes beyond human comprehension, he does it because he's a dick/it was funny/you deserved it. A proper shoggoth Exalt could presumably be done, but it's not Lunars. Or probably even fundamentally human.
At best, you end up with a superficial treatment that adds another poorly mixed element to the pot, resulting in an incoherent, ill-formed mess, kind of like this guy:
I suppose it's shapeshifting of a sort, but one shapeless blob is pretty similar to the next. Why throw out a rich mythological history of animal shapeshifting in favor of formlessness?
Nobody's suggesting that Lunars shouldn't be able to turn into animals.
There are certainly aspects to Lovecraftian monsters that don't fit the Lunar Exalted. But you could say the same about the traditional mythological monsters. Or animals. It's just a matter of picking and choosing what you include.
There's a lot in Lovecraft that's compatible with human motivations; shoggoths, in particular, seem to be after food and freedom.
I'll be more specific. Lunars should:
-Be able to take the forms of Lovecraftian monsters, assuming they pull off an appropriate Sacred Hunt.
-Be allowed to apply gribbly tentacular aesthetics to some of their Charms, if they so choose.
-Have Appearance Charms that make them look so horrifyingly wrong that people go mad.
-Be able to play with geometry and the flow of time a little bit.
-Not be harmed by seeing the visions of Oramus or other Lovecraftian elements of the setting.
-Have a variety of madness-related Charms, and perhaps a few that relate to dreams. In particular, they should have access to forms of madness that are arguably more
correct than sanity.
-Be able to spawn lesser monsters, whether that means breeding beastmen, breeding Deep Ones, turning people into werewolves, turning people into shoggoths, or whatever.
-Be able to inspire that specific fear I talked about earlier, of being a small brief mortal in a fundamentally indifferent universe, helpless and hopeless. Maybe with a specific intimidation-roll-booster.
Lunars should not:
-Have incomprehensible motivations.
-Be able to play with geometry and the flow of time a lot. My inclination would be to limit such effects to the Lunar's body and lair.
-Actually make the universe indifferent or hopeless.
-Be able to abandon their non-Lovecraftian side; a Lunar who turns into Cthulhu shouldn't be Cthulhu any more (or any less) than a Lunar who turns into Sue the Tyrant Lizard is Sue the Tyrant Lizard.
...
Now that I've gone into some detail about exactly what I mean, do you actually disagree? And if so, with which bits?