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.