In the case of miniature still-life set-ups it is possible to create lighting using LEDs. The level of light available is low and the technique is unlikely to be successful with anything but the smallest subjects.
LEDs generally create small, hard points of focused light, so it may be necessary to use a large number of lights to achieve the required effect. Nevertheless, the LEDs are cheap to buy. They also produce a cold white light which must be accommodated using the camera's white balance settings. They also have a poor colour rendering index so may not be appropriate for all subjects.
The lights weigh very little and can easily be attached to any support using tape, Blu-tak etc. They can also be used for small-scale light-painting. Fit an LED inside a small diameter tube and it can be used as a very focused light pencil that will draw lines in a light-painting image. The possibilities are limited only by imagination.