Your team desperately needs some type coverage. You can compensate with moves on other Pokemon but never underestimate the help that only STAB can give.
I would suggest using Snorlax as your Normal Type and Aerodactyl as your Flying Type.
In place of Clefable and Pidgeot, I would suggest using Jolteon (use a Thunder Stone to evolve your gift Eevee from Celadon City at Level 30 so that it gets Bite for some nice coverage) and Jynx (there's an an Old Man in the house next to the Cerulean City Pokemon Centre that you can trade a Polywhirl for that you can catch with a Super Rod in the pond on Route 6 between Saffron City and Vermillion City).
Since most of Lorelei's Pokemon are part Water Types, and most of Lance's Pokemon are part Flying types, Jolteon would be very helpful. A STAB Thunderbolt/Thunder combined with its high Speed and Special Attack stats makes Jolteon the perfect Sweeper for those two. It can also work well to take out both Lance and Gary's Gyarados' in one decisive blow because of the 4x weakness to electric attacks.
Jynx' STAB Psychic attack can be powerful tool against Bruno's fighting types as well as Agatha's all Poison team. In addition to that, as the last Elite Four member, Lance's Pokemon are really tough so STAB Ice Punce/Ice Beam from Jynx would be really useful.
My recommendations as to your team is as follows:
Item- Black Glasses
- Surf
- Ice Beam
- Bite
- Skull Bash
- Earthquake
- Megahorn
- Strength
- Brick Break
- Rock Slide (from the Move Tutor in Rock Tunnel)
- Iron Tail/Steel Wing
- Fly
- Hyper Beam\Double Edge (from the Move Tutor at Victory Road exit only if it has Rock Head)
Item- Leftovers
- Hyper Beam/Body Slam
- Shadow Ball
- Yawn (to put opponent to sleep whilst you set up Belly Drum and heal)
- Belly Drum (go to the Move Relearner on Two Island with 2 Tiny Mushrooms or 1 Big Mushroom that you can get off of any Paras or Parasect that you capture)
- Thunderbolt/Thunder
- Bite
- Double Kick
- Thunder Wave/Shock Wave
- Psychic
- Ice Punch/Ice Beam
- Lovely Kiss (to put opponents to sleep whilst getting Special Attack boosts from Calm Mind)
- Calm Mind