Why does this CO detector forbid the use of lithium batteries?

The only technical reason I can think of is that the discharge curves for lithium and alkaline batteries are different, and the low-battery warning might not activate at the same level with lithium batteries as it would with alkaline.

That's nearly it.

Alkaline batteries tend to exhibit a relatively smooth, gradual voltage drop, whereas lithium batteries will deliver a more constant voltage up until they're nearly discharged, at which point the voltage (and available current) will plummet. This is desirable for most applications, as it maximizes useful runtime. However, in a CO detector or other safety systems, it means that, by the time the device is able to sense that the battery voltage is low, there may not be enough power left to sound a low-battery alarm. As a result, the user may never notice that the battery has died -- the device goes straight from functional to dead, without passing through the intermediate state of low-battery beeps.

Also, devices designed to operate with Li batteries have a discharge control circuit to limit the battery discharge level - when the low level light comes on may be too low for the Li battery raising other safety issues.