Seeing as lulu is my favorite champion, it is not surprising that I developed the urge to play her in a solo lane, after playing her in every possible way I could think of, I realized that solo top lulu is actually really good. Maybe you will not trust my judgment at some points of this guide, like why I take teleport and ignite, or why I buy spirit of the lizard elder, but this is the build I find works, It is still not at its full potential but I think that solo lulu can be really successful with the right player.

When playing lulu top I quickly realized that I had no particular problem against any champion I went against in the top lane (even in a 1v2 scenario) ...Well playing against volibear can be a problem since you can't really do anything to him but yeah... Anyway, not to get sidetracked lulu's roles when playing solo are the following:
-Making the enemy solo top useless
-Helping your jungler get fed on your lane
-Being awesome globally (the reason for teleport)

Poke as much as possible, the first rule. Run away from everything until you think you can win in a fight. Once you are sure that you can burst your opponent down do one of the following:
-If you have ignite:
charge at your opponent, if he runs try to slow him if you are in range, if he is out of range, use whimsy on yourself and cast Help, pix on your opponent to assure a slow with glitterlance, as you chase use basic attacks and cast ignite if there is need for it.

-If you don't have ignite:
Try to bate your opponent somehow, when he starts coming at you attack him as much as possible and slow hit to avoid some damage. When he comes into melee range cast whimsy and kill him with your epic basic attacks and help, pix spell

Alternatively, if your opponent is ranged, poke at him and then charge just like you would in the ignite scenario.

When farming always try to just last hit, as I said earlier you need to get your jungler fed so pushing is not an option. Additionally you will have to use your basic attack only to farm and be really couscous while doing so. At any given time the enemy solo top may try to attack you so you will need to save your slow, speed up, shield so you can have favorable engagements. If you are under your turret there is no need to save slow but have whimsy and help, pix ready. Since you won't always be needing to use your basic attack, try to utilize your passive and all the on hit effect you will get through items to poke at your opponent. Lulu is really good at both poking and kiting and always try to take away your opponents life when there is no need for you to hit minions.

Since you will have teleport you will be epic globally, since you need your items to become good in the later game you should farm as much as possible and teleport into mayor fights to help your team with all the epic cc and utility that you have. In team fights use your ultimate on someone that dived or save it for your ad carry if you think it is necessary.

Pros:
-Great poke
-Great kiting ability
-Your jungler will have the easiest time ganking your lane
-Virtually undivable after level 6
-Turns around fights in you lane

Cons:
-Squishy
-People will say that you are a troll
-Can have mana problems early

You do not need to follow the runes, I'm not really the best at the game, which is why I think this is not the optimal build