As you explore the Underdark in Baldur's Gate 3, you'll eventually encounter the friendly Mind Flayer Omeluum at the Myconid Colony. He gives the quest Tell Omeluum About the Parasite which feeds into the Remove the Parasite main quest. He'll request that you collect two dangerous mushrooms from a nearby Arcane Tower in order to help him research your tadpole.
The Arcane Tower has some decent magical loot, and Omeluum rewards you with the Psionic Ring for your trouble, which suppresses your Illithid tadpole. With the ring on, you'll be unable to use your Mind Flayer powers actively in conversation, and it may have some play later in the story as things come to a head with your little passenger. The quest also has a lot of great story content, with a long sequence at the end featuring multiple skill checks that reveals more about your tadpole, and the tower itself is a stand-out set piece that's well-worth exploring.
But if you're having trouble getting past the Arcane Tower's defenses and figuring out how to get free reign of the place, you're not alone. I was quite stumped at first, but you have quite a few options for shutting down the Arcane Cannons, activating the Arcane Tower's elevator, and finding your Tongue of Madness mushroom and Timmask Spores.
1. How to get past the Arcane Cannons
The main entrance to Lenore's Arcane Tower is in the Southwest of the Underdark. You can reach it either by taking the fairy ring in the basement of Auntie Ethel's house, or by jumping across a small chasm to the southeast of the Duergar fishing village.
You're actually entering the Arcane Tower at its fourth floor—the structure extends downward from the main entrance into a canyon. The main entrance is guarded by four Arcane Cannons, two outside, and two inside, that will periodically damage you while you're in view. The main entrance to the tower is locked, but you can jump through an open window to the south of it.
The Arcane Cannons are heavily resistant to weapon damage, but there are a few ways you can deal with them. If Wyll or another Warlock is in your party, Eldritch Blast can take a decent chunk out of the Arcane Cannons' health. As long as you can tank their blasts, you can just brute force your way past.
Alternatively, you can use the spell Invisibility to just run past them—there's just one fight in the tower itself, and not only can it be avoided, you can only access it after you disable the turrets anyway. Don't be afraid to just send a Rogue or Bard in to explore the place solo.
2. Activating the Arcane Tower's elevator
The engine powering the elevator is at the base of the Arcane Tower, and you'll have to do some careful jumping to get there. From the main entrance, head out the southern door onto a balcony. From there, jump to the blue mushrooms to the east, then jump down to the balcony on the third floor.
There's another set of blue mushrooms farther below that will let you reach the ground level, but be careful—a jump down from here could hit you with heavy damage. Consider a spell like Misty Step to teleport down instead.
From here you'll be at the base of the tower. Collect one of the magic-nullifying Sussur Blooms from the garden out back and combine it with the engine inside the tower to reactivate the elevator, which you can access on the second floor up the staircase from the generator. Activating the engine also shuts down the Arcane Cannons, allowing you to reunite with your party if you snuck past them.
3. Finding Tongue of Madness mushrooms and Timmask Spores in the Arcane Tower
The mushrooms for Omeluum are on the third floor of the tower. Take the elevator up from the second floor after reactivating the engine. The Timmask Spores are on a bookshelf in the northwest corner of the third floor, while the Tongues of Madness are at the base of a giant orange mushroom to the southeast.
4. Dealing with Bernard, guardian of the Enchanted Tower
The Arcane Tower's top floor is guarded by a level 5 clockwork butler boss and his four weaker automaton friends. It could make for a challenging fight, but you could also talk your way into having free run of the place.
One level below, on the fifth floor, you'll find a book titled "The Roads to Darkness" in the southeast corner. If you read this book, you'll be able to quote lines from it when talking to Bernard the robot butler, which will make him recognize you as a friend. I don't know if you have to accept his hug to seal the deal, but why not let the poor sad robot man bring it in?
With all said and done, you can now return to Omeluum at the Myconid colony to learn more about the parasite, as well as secure his magical, mind-fortifying ring—just note that the ring can only be obtained by paying Omeluum a sizable sum, or passing one of a number of skill checks to offer him something of comparable value.