It depends entirely on which lovebird you mean
Lovebirds have a reputation for being sweet, cuddly taming projects, and a single hand-reared young lovebird often lives up to it, bonding closely to its person and learning step-ups within weeks. The same species bought as an untamed adult, or as a bonded pair, is a much slower project. Lovebirds pair-bond intensely by nature, and a bird whose social needs are fully met by another lovebird has little reason to work at trusting a large, reaching hand. So the honest answer is that taming is easy with the right starting bird and daily handling, and genuinely difficult, sometimes a matter of many patient months, with a wary adult or a settled pair.
Singles tame faster, and that cuts both ways
A lone lovebird directs all its social energy at its owner, which is why singles tame quickly and become the shoulder-riding companions in most videos. A pair is harder to tame but easier to leave during a working day, since the birds entertain and reassure each other. Choosing between those situations should happen before purchase, because adding a second bird later can redirect a tame single's loyalty, and separating a bonded pair to force taming is unfair to both birds.
The method that works for a bird this small
Lovebirds are tiny but they are proper parrots, and grabbing one in a fist to make it be handled teaches only that hands are predators. Work at the cage door instead: rest a hand nearby with a sliver of a favourite food until the bird approaches under its own power, then build to stepping onto a finger or a small perch for that reward. Females in particular can be cage-territorial and may lunge at fingers entering their space even when they step up happily once outside, so offering the door-and-perch route respects a trait that is normal for the species rather than a taming failure.
Bites, bluff, and the hormonal season
A lovebird bite is small but sharp, and a bird that learns biting makes training end will use it efficiently. Expect taming to wobble when a young lovebird matures and hormones rise; shredding paper obsessively, guarding a corner or a toy, and new sharpness from a hen are seasonal management issues, not the loss of your tame bird. Removing cosy hideaways and nest-like material, keeping sleep long and dark, and continuing the same gentle handling routine usually carries a household through that phase without starting again.
When a lovebird stays wild, adjust the goal
Some lovebirds, particularly older rescues with little human contact in their past, will accept company, take treats from fingers, and enjoy life near people without ever enjoying being held. That is a successful outcome for that bird, and continuing to chase and grab it in pursuit of cuddles only damages the trust you have built. If a bird injures itself panicking at hands, stops eating around people, or bites hard in genuine fear rather than warning, slow everything down and take advice from an avian vet or reward-based parrot behaviour adviser about whether illness or pain is part of the picture.
Small bird, specific knowledge worth passing on
Whether a particular lovebird steps up onto a finger or only onto a perch, which treat unlocks its cooperation, and whether it is a hen who guards her cage are facts a new keeper needs before the first handling session, not after the first bite. Keeping brief notes as taming progresses costs little and protects the bird's confidence through any change of home, and KinsLe Transferrable Profiles carries a lovebird's taming stage, preferred treats, and handling quirks to its next owner.