The First E4 Member you face is:
Will's Pokemon are around Level 40 to 42. He focuses on Psychic types but they all have a secondary typing which you can hit. You can use Lugia to take hits from his Slowbro and kill it, Typhlosion can be used to kill Jynx and Exeggutor, while you can use Tauros to kill his Xatu's. For Tauros you will need to teach him Rock Slide which can be taught to him via TM 80.
The next E4 member you will face is:
Koga's Pokemon are levels 40 to 44. He focuses on poison types so Lugia will be helpful here. He also has three Bug types which will be weak to Typhlosion. Your Crobat and Piloswine will both resist poison moves and provide good back ups.
The Third E4 member you will face is:
Bruno's Pokemon are levels 42 to 46. He focuses primarily on Fighting types. In this battle Lugia will beat pretty much everyone with STAB Aeroblast. Against Onyx you can use Piloswine who will have a STAB ground move, or Typhlosion if he has a grass move.
The fourth E4 member you will face is:
Karen's Pokemon are 42 to 47 and she focuses primarily on Dark types. However is is fairly diverse with Pokemon such as Vileplume and Gengar in the mix. You can use Typhlosion to get the edge on Vileplume and Murkrow, while slamming Umbreon with hard physical attacks from Tauros. Gengar you can hit with Crobat who will be able to outspeed and smash Gengar with hit of it's own, while Houndoom can be hit hard by a STAB ground move from Piloswine.
Finally you will face the Champion!
For this battle it will be useful to have Gyarados on your team with moves like Waterfall, Ice Fang, and Dragon Dance. If you have him at a high enough level you can set-up on Lance's Gyarados and sweep him with yours. An alternative would be killing his Gyarados with Lugia, and then sweeping with Gyarados. In anycase Lance's team is very Ice and Water weak, so if you can eliminate his Gyarados then you can spam a bunch of speedy high powered Ice and Water attacks. Piloswine will help against his three Dragoniteswhile Lugia or Gyarados can handle his Charizard and Aerodactyl with their water moves.
Best of luck with the league!