In my experience, the Lithium DL123A batteries will maitain the white brightness for far longer than any alkaline batteries could. They do get a bit dimmer after the 1st 5-10 minutes.
When they're nearly used up, they will produced a more yellow light, and then quickly die. It's important not to run them once they've died cos they can damage the lamp.
If used in short bursts, the DL123As can last longer as they recover some of their charge. Lithium batteries have a very good ability to maintain charge up until the last second. They also last longer in colder temperatures while alkines will fail at zero-to sub-zero temperatures.
Alastair