LUCA likely had a very simple, leaky membrane or a rudimentary protein shell. Bacteria developed a cell wall made of peptidoglycan (a mesh of sugars and amino acids). This acts like a reinforced chain-link fence, allowing bacteria to survive in different water pressures without exploding.
The peptidoglycan wall of sugars and amino acids is exactly what penicillin attacks! If a cell has this specific wall, it’s a bacterium.