Building my Team

Currently have 6 badges. Before I go get the other two and face the Elite Four, I'm spending times building and raising my team.

Here's what I have:

Houndoom
Level: 38 (Almost 39)
Ability: Flash Fire
Nature: Timid
Moves:
Sucker Punch
Bite
Fire Fang
Destiny Bond

Lapras
Level: 45
Ability: Water Absorb
Nature: Docile
Moves:
Water Pulse
Brine
Ice Beam
Surf

Talonflame
Level: 50
Ability: Flame body
Nature: Modest
Moves:
Flame Charge
Acrobatics
Fly
Peck

Delphox
Level: 51
Ability: Blaze
Nature: Bold
Moves:
Fire Spin
Mystical Fire
Flamethrower
Psybeam

Lucario (Holds Lucarionite)
Level: 47 (Almost 48)
Ability: Steadfast
Nature: Hasty
Moves:
Power-Up Punch
Swords Dance
Aura Sphere
Bone Rush

Charizard (Holds Charizardite Y)
Level: 52
Ability: Blaze
Nature: Lax
Moves:
Fire Pledge
Dragon Rage
Flamethrower
Flame Burst



I am willing to change Talonflame and/or Delphox if needed.

You have 4 fire types on your team and I don't think you need them all. I would say you keep Houndoom but change its movepool. Its nature is good but you need special attacks to make it work :)

Agreed that having 4 fire type Pokemon is a bad idea. I would give the Charizard Flamethrower, Solar Beam, Air Slash, and Fire Blast/Roost. Charizard Y is a very strong special attacker whose ability strengthens fire type attacks, weakens water type attacks and makes Solar Beam attack in 1 turn. Air Slash is a strong STAB move. In general, you want to try to get more type diversity in your Pokemon or at the very least out of their movepools.
Give Lucario Earthquake instead of Bone Rush, and Close Combat would be a better choice than Power Up Punch since you have Swords Dance. And Aura Sphere is unneeded if you're using him as a physical attacker.
I'd try to fit a good Grass and/or Electric type Pokemon on your team to deal with their glaring water weakness.