Are you sure the lights are an alternator issue? It probably is, I had my tachometer (RPM) dip to zero when my alternator was breaking, in addition to the battery warning light on the dash lighting up. Also, what lights are dimming? Headlights, interior? Over bumps? All the time? Randomly? Sorry for so many questions, but they could all have a different casue and have the same dimming effect.
So first, I would make sure its the alternator going bad, not a battery, and not just some loose wires. Second, changing the alternator is really easy. You unscrew the wires from the back, take out the main bolts and rip her outta there (well, I sorta lied, this is the hard part, lol, because you have to get a really big screw driver/crowbar and pull the belt tensioner down so that you can get some slack on the belt that runs on the pulley of the alternator, then you can rip it out and put the new alternator in). Just for the sake of not screwing up, you may want to have another person there to help push the belt tensioner down/someone who has worked on replacing an alternator before, you dont want to strand yourself in the drive way!
LoL, oil leaks.....yeaaaaaaaaaaaah, one its british, two its a land rover....result: it is going to leak! The entire bottome of my D1 is caked in oil--i really should power wash it, but I am afraid to get our wonky electronics wet and have me stranded at the car wash lol--as long as you are not dropping puddles of oil, you should be fine. Just keep an eye on the dipstick if you feel uncomfortable, our danged trucks hold like 7 quarts of the stuff, but its never good to run oil low.