How do I make a Leek foam from Agar or Egg Whites? I have tried 4 times now and either the foam never truly stands up or there is too much agar and the thing starts to harden.

I only have agar or egg whites. I don't have any lecithin powder. What I am doing first is creating a leek juice. I have tried it a couple ways. One is to stick a bunch of leek bottoms in a Cuisineart. Then I cook for a few minutes, strain through a cheese cloth and let cool. I take about 100ml of that "juice" (once it is cooled) and add in about 1 gram of agar. I have tried 1.) beating it in a bowl by hand 2.) mix it, then heat it, then beat it by hand. Both ways fail.

I also tried with egg whites. Same procedure for the juice, but I added in 1 egg white per 100ml. Way too runny. Would never foam. I then added in 2 egg whites. Still never foamed. I even added a 1/4 tsp of sugar. Nothing. I also want this to taste like Leek, not eggs ;)
Agar is basically just a gelatin. Lecithin is a surfactant and emulsifier, which is what you ideally need for your foam. The agar probably isn't sufficient to create the necessary tensions between the oil and liquid and when you introduce air into the mixture it isn't being held in suspension, which is why your foam isn't 'holding up'.

I'd strongly recommend trying lecithin along with a more vigorous air injection method such as an electric hand blender.

I don't believe it's anything do with your leek jus, but your method of foaming.

There's a useful article on this here.