Yeah, like Dale says, sometimes there is nothing you can do. Around the dew point, you will get condensation. Grass, leaves, and other plant growth (even fungi) will all transpire or breath, putting moisture into the air. Wet ground can contribute to it, even if it appears dry for the first inch or two. Breathing under a tarp adds moisture to the air. Generally, when the entire area has condensation, your tarp will, too. No amount of ventilation will protect you under all conditions.
Even a double walled tent will have condensation. But, body warmth will drive a good majority of it to the outside layer. Second nights can be a problem, though. But I have had frost over everything in my tent, too. One of those things you just deal with the best you can. Usually this means a delayed start, opening up as much as possible to dry stuff off. Or, if it is real early, just packing up shaking it off, and drying what you can with a bandana. A fire in the morning helds quite a bit, adding warmth to the surrounding air and raising the dew point, hence evaporation rather than condensation. This is where a lean-to pitch can really help, since it is set up near a fire.
Would a lean-to help over an A-frame? Sometimes slightly, sometimes not at all, sometimes a lot. Depends on the exact conditions. Would a ground cloth help? Again, maybe. Plastic or cuben would have helped. Silnylon, not so much. Tyvec, less than silnylon. Even plastic sheets will bleed moisture vapour. Silnylon will hold water, but will not stop water vapour from penetrating(set a water filled bag on top of some raw wood.) Tyvec is designed to allow a house to breath moisture out (since you never trap insulation between two moisture barriers in a wall.) A PU coated ground sheet or tent foot-print will stop a lot of it. It depends.
Basically, sometimes, you end up getting a lot of condesation with a tarp. Is it better than a tent? Depends on how you look at it. Usually the total amount is less. Some will say you get less with a double walled tent, but, you usually get at least as much; you just don't notice it on the inner body so much. Some will say it is easier to deal with using a single walled tent, just wipe it down. With a tarp, you can just shake most of it off. But, I hate to carry dead weight.