EFAs are essential fatty acids (omega 3, 6 and 9), and are possily the best thing you can take for your overall health and wellbeing. Even if they end up doing nothing for your hair they are worth taking!
I personally rate Udo's Choice Ultimate oil blend (you can buy in cap form or just liquid - i don't recommend caps as you'd have to suck down millions of the buggers... i buy this
http://www.amazon.co.uk/Udos-Choice-Ult ... pd_sim_d_1) look at udo's website here too
http://www.udoschoice.co.uk/ where you can find out a lot about it.
I don't know if you work out or anything, but i just pop 3 desert spoons into my morning protein shake.... easy! It's something I have always meant to take regularly but it's been off and on, mostly crappy supermarket capsules which are pretty much worthless. I just started taking Udo's regularly a few weeks ago so we'll see how it helps. Already noticed better complexion though.
My personal feeling is that revita is much better than nizoral... but then it's much more expensive. I can use it everyday (actually leaves my hair feeling really good) and it has a lot of other goodies in it which may or may not help but can't hurt to try. Mostly I find the additional caffeine and emu oil very interesting... I use that in the morning, then tea tree and mint (soon to change to lavender like yourself) in the evening.
Finally you could try one of sinere's minoxidil solutions - the reason why i personally like them is that the have anti DHT components such as sophora flavens, and additional growth stimulants like adenosine (ups FGF7), creatine and so on. It's a convenient anti DHT and growth stimulant topical in one. Then assuming the minoxidil sulphate stays stable enough to last you have all the potential benefits that brings, if not then at worst it's just a 4% minoxidil. Just a thought!.
Have a read of this
http://immortalhair.homestead.com/files ... s_Book.htm
There's a lot of good info there, and while you'd probably have to be certifiably insane to do/take everything there you may find one or two things that you might want to give a try. There's a good bit on EFA's and how they can help in there too which you might find interesting. It's a long read but worth it to increase your understanding, that way you can make more informed decisions on what products to use to best suit you.