Charisma synergy for saving throws is the only significant benefit you would receive from 3 free levels of Paladin.
The Paladin's Divine Grace ability is very strong, and works well with a character who invests in Charisma to increase saving throw DCs, like a Warlock. However, most of the other things you've mentioned are either unavailable to you or their benefits are so small they're basically irrelevant:
- Warlocks can't cast spells in heavy armor by default. The Paladin's proficiency in medium armor would allow you to wear mithral full plate, but this is only 3 AC better than a mithral breastplate, which your Warlock could wear even without Paladin proficiencies. Not a big enough difference to worry about
- Paladins can't summon a mount until 5th level, so this isn't available to you.
- The healing from Lay on Hands is based on your Paladin class level, so with only 3 levels it provides trivial amounts of healing.
- Paladins don't gain the ability to cast spells until 4th level, so this isn't available to you.
- The other bonuses you receive from Paladin (immunity to fear and disease, Smite Evil, Detect Evil) vary from nice-to-have to basically useless.
Overall, this is only moderately valuable to you. Saving throw bonuses are good, but that's essentially the only useful thing you're getting. In my opinion, it's not significantly better or worse than getting Evasion and 2d6 sneak attack from Rogue (note that Sneak Attack works with Eldritch Blast, as long as you meet the other requirements for triggering it).
If the Paladin levels aren't free, this is a bad deal.
The above section was written on the assumption that the three levels of Paladin are essentially free, as if you were getting three levels of gestalt progression but then returning to single-class progression at level 4, which is my understanding based on your comment.
However, if this isn't the case, taking a 3-level Paladin dip isn't worth it. You would much rather be a 6th level Warlock than a 3rd level Paladin/3rd level Warlock.
Paladin of Tyranny might be a better choice if it's allowed, but watch out for its code of conduct.
The SRD's variant character classes include an evil Paladin variant, the Paladin of Tyranny. In addition to the saving throw bonuses, this variant also receives an aura that lowers enemy saving throws. This is quite good for a Warlock, and would tip the balance toward Paladin being a good choice for your "subclass."
However, the Paladin of Tyranny has a code of conduct that makes it very difficult to play in an actual game (basically "be as tyrannical as possible 100% of the time"). If your DM chooses to allow this class, consider working with them to come up with a less ridiculous code of conduct that will allow you to play the class without ruining the game for everyone else.