You're right, there's not a lot of synergy there. Out of combat, your Warlock will add a lot of utility with his less combat-focused spell list and his ritual abilities, but in combat, you have 2 potential paths:
- Focus on your Warlock levels to become a powerful spell caster. Going this route, your Paladin levels will add heavy armour and a shield, which will help you stay alive and allow you to dump Dex. It's not much, but it's something.
- Focus on your Paladin levels to become a powerful melee fighter with spellcasting abilities that supplement your fighting skills. Going off what you've said, I'm going to assume you're taking this route, and the rest of my answer will focus on that.
So, let us take a look at the Paladin. The Paladin is already something of a hybrid class, with some spellcasting supplementing its fighting abilities. This synergizes better than most other hybrid classes, because the Paladin spell list focuses on bonus action spells that boost the damage of your attacks. Sadly, most of these require concentration to use.
So what can the Warlock offer the Paladin in a fight? (Preferably without investing too many levels.) There are a few things.
The first is a good ranged option. Unless you invest in Dex, the Paladin's only ranged option is throwing weapons, which suffer from extremely short range and being both heavy and expensive to carry a lot of. The Warlock's Eldritch Blast scales well with level, and that's character level, since it is a cantrip, so your Paladin/Warlock should always have something to do if he can't or shouldn't get into melee. If you take the Agonizing Blast invocation (and you should), the damage of Eldritch Blast should be reasonably comparable to your melee damage. Repelling Blast is not as good for you as it is for most Warlocks, because you will generally want the enemy to be coming closer, not further away. Eldritch Spear pretty much guarantees that if you can see it, you can hit it.
The second is what has come to be known as the Darkness + Devil's Sight cheese. If you take the Devil's Sight invocation, you can see in magical darkness. Then you cast Darkness on an object on your person, and you get a 15-foot sphere where you can see perfectly and most enemies can't see at all. Or, to put it differently, your melee attack rolls have advantage, and anyone trying to hit you in melee without special sensory abilities has disadvantage. With the Sentinel feat, this becomes ridiculously mean, because the only viable option for a creature in this situation is to run, and your opportunity attack will not even let them do that. This is probably the best thing your Warlock levels can offer you by far.
The final thing is that Warlocks have access to some good low-level defenses that don't require concentration. Mirror Image is a great defensive spell that stacks with everything and doesn't require concentration. Armor of Agathys does not scale all that well, but at low levels it definitely helps. And Arms of Hadar is a great spell if you're surrounded, because you can prevent some or all of the opportunity attacks you would normally incur.
All things considered, I would probably either recommend 4 levels of Warlock, which will get you the Devil's Sight and Book of Shadows invocations as well as the Darkness spell (among others) without losing an ability score increase (these are extremely important), or 8 levels, which would get you Devil's Sight, Book of Shadows, Agonizing Blast, Eldritch Spear, and Darkness, without losing an ability score increase. (Obviously, there's more to it than that, but those are the synergistic bits.)