Starting a fire with a lens without the sun I am curious about the ability for a lens to start a fire without using sunlight. Is it possible for alternative light sources (LED, incandescent, etc.) in combination with a very large Fresnel to start a fire? Or more appropriately how much energy could a very large Fresnel lens concentrate into one point using everyday light sources?
In considering different types of light sources, which would be best for generating the most heat? Luminous efficacy and the size of the light source seem the most obvious but how would the color of the light affect the lens' ability to generate heat?
Will a high focal length and large aperture lens (such as a giant spot Fresnel) even be able to focus the amount of light sources necessary into a small enough point to generate enough heat?
 A: You can't focus light onto a region so that it increases the temperature to a value larger than the temperature of the source. This has its origin in Fermat's principle, and since it is a variational calculus it carries to much of physics. This is primarily Lagrangian and Hamiltonian mechanics. The fundamental upshot is that the volume a system occupies in phase space of position and momentum is an invariant in conservative systems. The optical analogue of this indicates one is not able to concentrate light from a source and heat up a target material to a temperature larger than the source.
A: When you use a lens (or a focusing mirror) to increase the "power" of a light source - whether it be the sun, or another light source - what you are really doing is making the light source "look bigger". Which is a lot like "being closer" to the source. 
For example, if you say the sun normally is a disk that spans about 0.5° in the sky, then if I have a lens that makes it look like it's 5° across, the area is about 100x larger (diameter squared), and the energy flux will feel roughly "like the power of 100 suns". I say "roughly" because there are inefficiencies in lenses and mirrors.
The same principle can be applied to any other light source - when you make the light "seem bigger", the net effect is the same as that of "getting closer" or "having more lights". This means that the question of whether you can use a lens to cause something to catch fire really comes down to this: if you got really close to your light source, would the thing you are trying to set fire to catch fire? If the answer is "yes" (like it is for the sun), then you can use a lens to "make it look like you are that close". If the answer is "no", then a lens won't help.
Specifically, it is not possible, with lenses / mirrors, to make an object hotter than the light source you are focusing. This is explained in more detail in this earlier answer
One thing to note - light bulbs have a minimum distance to the filament (the bulb has a certain size) both to keep the glass from getting too hot, but also to lower the risk of things catching fire because they are too close to the filament. However, it is quite easy, with a lens, to "make it look like you are really close to the filament". In other words, a decent lens (that is, a lens with sufficiently low f number1) should be able to focus a filament of an incandescent bulb onto a piece of paper such that it can burn a hole in it.

1 The f number is the ratio of the focal length of a lens to its diameter. The lower the number, the bigger the lens - and the more light per unit area it collects.
A: It is very dependent on how well your target absorbs (rather than reflect) the light and converts it into heat, and how well that material conducts heat away if heated in a small spot - black, matte cardboard for example will absorb most of the energy from visible light and convert it to heat. Losses will still occur from blackbody IR radiation and surface air cooling.
In practice, one watt of energy concentrated into a few square mm (think overheating a very small resistor with 1 watt of electrical energy, with flammable vapor present) can start a fire.
LEDs can reach efficiencies in converting electrical energy to optical energy of several 10s of percents, so actual optical power is in the same order of magnitude as input power...
Ignore constraints that assume that all light is generated from blackbody radiation, unless your light source is working on the basis of blackbody radiation (an incandescent lamp does, a LED or CFL does not!).
