The warlock's Thirsting Blade eldritch invocation cannot be normally used with the (non-warlock) class feature Extra Attack, since both feature explicitly say you attack twice instead of once. But it seems to me that you could use both features (if you have them) when using Two-Weapon Fighting.
Assume your character is wielding two light weapons, one of which is your pact weapon. You take the Attack action on your turn to attack twice with your non-pact weapon using your Extra Attack class feature.
Then, given the Two-Weapon Fighting rules, you use your bonus action to attack once using your pact weapon this time.
The Two-Weapon Fighting rules (PHB p. 195) state:
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand.
But since your have the Thirsting Blade invocation, and you used the Attack action, you get to attack twice with your pact weapon.
The Thirsting Blade eldritch invocation (PHB p. 111) says:
You can attack with your pact weapon twice, instead of once, whenever you take the Attack action on your turn.
Does this combo work within the rules, or is there any interaction I'm not aware of?
Best Answer
No.
Or, more specifically, yes, as long as you didn't get those features via multiclassing, which is never.
The multiclassing rules state:
Since you only get Extra Attack as a Warlock if you multiclass and you only get Thirsting Blade as a non-Warlock if you multiclass, this rule always applies and you can never use them together.
Furthermore, even if you did find a way to get them both from a single class, you couldn't use them with two-weapon-fighting like that because the bonus action attack from two-weapon fighting isn't an Attack action. You could, however, use them together in that case despite the 'twice' language to get three attacks out of a single attack action without issue: just make your first attack with something other than your pact weapon and then use your pact weapon via Extra Attack and then use it again via Thirsting Blade. Again, though, you can't actually do this because no class has both class features and they don't stack when you multiclass.