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I once got solo top as Lux, and again as Anivia. I'm certain this is contrary to the established meta, but I found it better to just hug the turret and call in ganks... which is applicable to any champion who finds themselves in this situation.
However, I found in both situations the Jungler offered me blue buff fairly early on(In the case of a purple spawn, you may need jungler to instead hold your turret while you go get blue with the aid of one of the two bots if your champ isn't able to solo it quite then), I was then able to maintain a decent farm through ability spam and manage to soften the aggressive champs up a bit leading up to the jungler's gank. I'm not sure if this works for most champs since I was using a mage for those incidents and not the typical bruiser top.