Sha Lin is the ultimate way of telling you to get out of the sky - and when you're on the ground, Impaler Arrow is a huge threat for you. Resilience will be necessary; a good Sha Lin will deal too much damage for Haven to be effective.
Try to avoid close combat with Lex. In this situation, it’s best to lob bombs from him at a distance. If you do end up in a close situation, Accelerant is a good choice to keep him down.
Stun'Damba is key here. If you can buff up the range of Snake Toss, fighting fire with fire can really hit Bomb King hard early-game - and late-game if he doesn't buy Resilience.
Contrary to what you may see here, setting your rune in the enemy's line of sight can work to your advantage if you have the Inner Strength legendary. The enemy expects you to be weak and on cooldowns when you return to your rune.