As the title says, i've been wondering whether it's more time/ cost efficient to stack lucky picks to help me farm up for larger items before selling them on or to simply go straight for the items in question, component by component.

Then surely this is quite simple you say - simply work out how much money you can get from the lucky picks vs their cost and work things out like that. There is a complication: you are generally more powerful if you go for the item componants -> lucky pick gives you straight ap and not very much of it per gold in comparison to pure ap items like blasting wand. So how significant would the extra kills/last hits you might get be? Obviously by adding this in, I'm destroying any chance anyone has of coming up with a definite answer, unless it's more cost effective to get item componants anyway.

An example of this is my Katarina build, it's pretty standard:

Dorans shield
(don't make an issue of this, I find the extra up front survivability allows me to be more agressive if going for a kill and gives me a better chance to get out as well, despite the lower long term prospects for my average hp. Also I can get a health potion which is handy for living longer than I should)

Sorceror's boots
(boring, very standard, will have it pretty sharpish in a two man lane)

Mejai's Soul Stealer
(Again pretty standard, will have this by level 7 or 8 if things go well in my lane, alternatively I can go for 3 lucky picks at this point and get the book at level9-11)

Rylai's
(This is the problem item, I tend to get Rylai's 11-14 can't really be sure whether or not the lucky picks are worwhile getting... They're probably more reliable as an income source than I'd be otherwise however, the componants of Ryali's are pretty good for keeping me alive/killing things)

Lichbane
(From here on I don't have enough lucky picks left for it to matter)

Zhonya's ring
(just here cos I wanted to finish off my build.)

Another thing to take into account is what champion your using. Ive been playing around with all the gold over time stuff with Allistar. Why? I find he ABSOLUTELY blows at last hitting. Keep in mind I main Kassadin and I last hit fine with him.

I still havnt decided if its worthwhile though. Things like people killing dragon while I dont notice or how many towers are down really changes things from game to game.

With many casters I don't really feel it's necessary to get Lucky Picks because as the games go on you tend to be overshadowed by the carries/tanks. So when I play an AP build Im usually trying to get the items I want as soon as possible to gank and get my kills in.

Alright after a day's worth of research into this, I've come to the conclusion that the choice of lucky picks is situational! (Yay for cop out)

If you have a good early game and are looking ready to rack up a high score then go straight for mejai's it will cement your advantage far faster and the money from kills should make up for the lack of income from the lucky picks. If however you have a bad early game, lucky picks mean that you'll gain income at a reasonable pace despite a lack of kills and should be taken if you're aiming for a late game smashing aka veigar because in the long run you'll get the higher tier items you need for really high damage earlier although the item bought immediately after the lucky picks will be dleayed somewhat

I wrote up a rather extensive guide some time ago... Until I locate it, here are some rules of thumb: you never need more than two unless you can afford them really early, never sell them until they can pay for a complete high-end item, and taking Greed mastery and Avarice runes makes all cash items much better.