You should be a few levels above Tate & Liza, not at their level because it's a double battle, meaning they can target one of your Pokemon simultaneously and KO you quicker.
The best thing to do is use Swampert and Absol against Tate & Liza, and teach Absol Shadow Ball, since Ghost is physical in Gen III and Dark is special. Not sure if you get the TM before them or not, so if not, then get Sableye since it learns Shadow Ball by level up. Absol also only gets Bite, which is really rubbish.
Swampert should use Surf, since it won't hit your partner and hits both of your opponents. They also have 3 Pokemon weak to water, so go for that on Swampert. Sableye/ Absol should use Shadow Ball constantly. Light Screen might be set up so watch out for that, but Shadow Ball will bypass it being physical. If you have, give both of your Pokemon a Chesto Berry because Lunatone has Hypnosis.
Watch out for Solrock, because it packs Sunny Day and Solarbeam, but it doesn't have STAB and Solrock has rubbish base 55 sp. atk, so I think Swampert should be able to survive one hit if it's a few levels above.
Xatu will try and spam calm minds and/or use confuse ray, and it'll proceed to sweep you if you let it set up. Do whatever's possible to get rid of Xatu first. If Absol still has Taunt, use that against them to prevent set up.