My first thought is that door microswitch is not working which is the most common thing which happenes.
Is it the same situation on both doors?
Lucas alarm box operates the interior illumination: 2 footwell lights and rear view mirror 2 lights. On rear view mirror you can flip the switches to check if the bulbs are fine or not, but do check footwell bulbs.
Under steering wheel fusebox, fuse number 12 rating 15 amps powers the lights, so I would check and replace that as well (it powers the boot light as well, however resistance on it might be too high and could light the boot, but cannot power 4 bulbs in the interior).
If all is well then we might think you have some break in the line from alarm box to the interior lights.