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Nexa and Proove PIR sensors, they function on battery. And it lasts about a year, as I understand. However, would they work longer if I use lithium battery instead? I would not like to change a battery every year..

Check the specifications for the lithium battery, it's the battery's mAh that determines how much energy/capacity it has and also how long it will last. Normally I would say the lithium battery has more capacity than a alkaline type of battery, but it comes with a price tag.
You could also consider removing the indicator LED in the IR detector and thereby saving some energy every time the IR detector is activated.