For the aïoli: Pound garlic with a mortar and pestle. Add salt and smash the last solid bits of garlic. Add egg yolk and stir with the pestle to amalgamate the mixture. Using the pestle, work in oil, a cautious trickle or a few drops at first, then gradually increasing the flow as the yolk becomes tacky and opaque. As the yolk reaches saturation, the mixture will make a satisfying clucking sound. Adding a few drops of water to the aïoli will whiten and soften it, allowing you to add more oil, which you may choose to do if you find the garlic remains too aggressive.
For the fritto: Heat oil in a large heavy pot over medium heat until temperature reaches 365°–370° on a candy thermometer. Meanwhile, pour buttermilk into a wide shallow bowl and set aside. Combine flour and semolina in a wide shallow pan and set aside. Line 2 large sheet pans with parchment paper and set aside. Dip celery into buttermilk, then transfer, dripping, to the flour mixture. "Shimmy" the breading pan so that the pieces settle, coating their sides, then flip each piece to coat other side. Lift out breaded celery, tap to remove excess flour, then transfer to prepared sheet pan without stacking. (This simple coating is never uniform and does not need to be. Ideally, the breading will have wrinkles and some barely coated spots.) Repeat breading process with lemons, then with squid.
Add a few pieces of batter-coated celery at a time to the hot oil without crowding. Fry celery, undisturbed, until a pale golden crust sets, 1 1⁄2–2 minutes. Using tongs, very gently turn any pieces that won't otherwise brown on the top. Don't fuss with the frying food; the fragile breading must stay integral, or the fritto will go limp and become greasy. Once golden, lift out the pieces with tongs or a mesh skimmer, dangle them briefly over the oil to let drip, then set gently set on paper towels to let drain. Repeat frying process with lemons, then with squid, frying lemons for 45-60 seconds, squid rings for 1- 1 1⁄2 minutes, and tentacles for 45 seconds.
Season fritto lightly all over with salt, divide between warm paper napkin-lined plates, and serve with aïoli.