Lapulapu is strongest at levels 1-3 (his base damage is high) and level 4 (his ultimate spike is massive). He's weakest at level 2 (before he has all three abilities) and when his Heavy Blade stance abilities are on cooldown.
The counter-intuitive tip: Lapulapu wins most level 1 trades, but he's vulnerable immediately after using his abilities. If you can bait his Skill 1 in Twin Blade stance, you have about 6 seconds where his damage is significantly reduced. That's your window to trade back.