As Kane and the safecracker head into the basement to get at a special, high-security safe-deposit box (and to blast their way through half the bank's security guards in the process), Lynch stays on the ground floor to guard the hostages and fend off any would-be heroes in the form of guards and cops. Here's where things diverge dramatically from the action in the single-player mode; while you won't always be able to keep an eye on Lynch in single-player, co-op gives you a unique chance to see things from his perspective. And because Lynch is a medicated psychotic who's prone to rage-fueled blackouts, you'll get to see the things he can't remember.
Case in point: as Kane and the safecracker finally blow open the vault and gather up the briefcase they were sent to collect, something horrible happens upstairs - Lynch is diligently guarding the hostages, when suddenly he's surrounded by cops. Some of them are real cops, who are actually shooting at him, while the rest are the hostages, whom Lynch is absolutely not supposed to kill.
The thing is, Lynch can't tell the difference, and neither can you. As Lynch goes into full-blown murder mode, the hallucination intensifies; some of the cops' faces change to pig heads, and his vision shimmers like a mirage. And that's how Kane, horrified, finds him when he emerges from the vault - madly firing into the corpses of bank employees and customers. It doesn't matter, though; the pair have what they came for, and - as SWAT teams descend on the massacre, Kane, Lynch and the safecracker escape in a waiting van.