It's nice to see you're doing your research.

I'm not sure where you're seeing that seed diets are recommended for lovebirds but a seed diet is not good for any type of bird.
There's several problems with a seed diet but here's just a couple:
1. It's nutritionally deficient, can lead to malnutrition, and can cut a bird's lifespan in half.
2. The birds will pick through the seeds and only eat what they like "best" which is usually the high-fat stuff (sunflower seeds, for example). It's kind of like if you offered a kid a plate with celery and cake, and they're just going to sit there and eat cake until they're full.
3. The vitamins are sprinkled on top so there's no way of knowing whether they're getting enough or, possibly,
too much.
Now, I know you're talking about feeding a seed diet supplemented with vegetables and while that's better than a seed-only diet it's still not going to ensure that the bird is getting proper nutrition.
The reason why pellets are the best choice is because they are completely nutritionally balanced and the bird can't "pick through" the food and eat what it wants and leave the rest. With a pellet every bite contains the same, balanced amount of nutrients.
Even with pellets you'd still want to feed some fresh fruits and vegetables but the pellets should make up the vast majority of the diet and the fruits and vegetables should be fed very sparingly.
Not all pellets are created equal. Avoid the ones with food coloring and sweeteners.
Michael uses Roudybush which is a high quality, non-organic pellet. Definitely read Michael's blog post on
Roudybush Pellets because he goes into great detail about parrot diet, why pellets, how pellets affect a bird's health and plumage, why he chose Roudybush, etc.
I use
Harrison's because it is high quality
and organic, but because it's organic it costs more and must be used within six weeks of opening as it has no preservatices.
In Michael's blog he outlines a few reasons why he thinks the extra cost of organic pellets isn't "worth it," and definitely be sure to read his thoughts there, but organic vs. non-organic is a personal decision and to me it
is worth the extra cost to know that my bird's food does not contain pesticides, preservatives, or GMOs.
I'm not saying that I'm right and Michael is wrong, I'm just giving the reasons why I choose Harrison's. That being said, you can't go wrong with Roudybush, either.