Why
The ASPCA lists lemon, lime and grapefruit as toxic to dogs and cats. Essential oils (limonene, linalool) and psoralens, concentrated in the peel and plant, can cause vomiting, diarrhea, lethargy and light sensitivity of the skin. A lick of the flesh rarely causes serious trouble, and most pets dislike the sour taste anyway, but there's no benefit to feeding it. Cats are especially sensitive to essential oils, so citrus aromatherapy oils should be avoided too.
How to give it / if eaten
Don't offer it as a treat. A small lick of the flesh can usually be watched at home, but call your vet if your pet ate a lot of peel or seeds or licked citrus essential oil. Keep lemony dishes and citrus diffusers away from pets as well.
Watch for these signs
Vomiting, diarrhea, drooling and lethargy can occur. Larger amounts or essential oil exposure may cause wobbliness, skin rash or sensitivity to sunlight.
FAQ
Mandarins are okay, so why be careful with lemons?
Mandarin flesh is milder and sweeter, so small amounts are generally considered fine. Lemons, limes and grapefruit are more acidic and richer in essential oils, and the ASPCA lists them as toxic, so it's safer to be stricter.
Are lemon-scented cleaners or air fresheners dangerous?
The scent alone usually isn't a problem, but licking or applying concentrated citrus oil can be. Avoid essential-oil diffusers around cats in particular.
General information only. Weight, age and health conditions change how a pet reacts, so ask your vet if you are worried.