You do have to watch out for those tricky multiclassing rules. Oddly you can happily start out as a paladin with 8 dex, you just can't MC into one.
You also can't MC out of one. You must meet the multiclassing requirements of
all your classes, including the ones you already have. This is a change from how multiclassing worked in the playtest.
Ninja'd. Warlock is the only class that doesn't penalize Melee characters for multiclassing. The level 5 invocation is available based on character level, so fighter 1, warlock 4 gets Thirsting Blade.
This also is not correct. Even though you meet the level requirement, there is no way to get Thirsting Blade at fighter 1/warlock 4, because you don't get a new invocation at warlock 4! Your invocations come at warlock 2, 5, 7, 9, 12, 15, and 18. And you can't take Thirsting Blade at warlock 2, because it requires the Pact of the Blade, and you don't get your pact boon until warlock 3. There is simply no way to get Thirsting Blade earlier than warlock 5.
To the OP: If you want to go paladin/bladelock, Strength should be your top stat, then Charisma, then Constitution. Put your first level in paladin (for heavy armor), then your next five in warlock. After that, you can either stick with warlock for the rest of the game, or throw in more paladin levels to taste. If you choose the latter, it's best to arrange things so that when you hit level 12, you are either paladin 5/warlock 7, or paladin 3/warlock 9. That way you can pick up Lifedrinker on schedule.
Dexterity is a paladin-bladelock's natural dump stat. You have to have 13s in Charisma and Strength for multiclassing, and you need a solid Constitution if you're going to be a front-line fighter; unless you rolled stats and did amazingly well, it's going to be tough to pump Dexterity too. If you want to go the Dexterity route, fighter/bladelock or ranger/bladelock would work much better.