I thought to make a simple tealight suitable to be used with any thing (figure, lamp etc), that could be easy implemented to any kind of these and finaly made one.
Here is a video of it working
https://www.youtube.com/watch?v=dny12pFuBjk
https://www.youtube.com/watch?v=ufys6ERe9i8
This tealight is quite big and uses AA battery (planning to make 2xAA ver. in the future), and also a simple Joliethef for powering the led.
Here is what you need to make one of these (list of what I used):

• paper clips or any other wire that is springy and may be used as a battery contact (check the resistance of the wire - less is better) - make a battery springs of it that will fit (I'm planning to add a spring making tool later for easier making)
• AA battery - 1pc
• LED - I used these for changing colour RGB http://s.click.aliexpress.com/e/f0ulA0p and these as a white warm steady light version http://s.click.aliexpress.com/e/bXzv1okp
• on/off switch - project using these switch http://s.click.aliexpress.com/e/ffyDCvL
• some parts for jolie thief like these:
  • toroid core http://s.click.aliexpress.com/e/1I9xSDj
  • npn transistor here is an example http://s.click.aliexpress.com/e/crJhiflP, you may also use PNP depending on the jolie thief ver.
  • resistor from range 1K-20K (less resistance more light but also more power is being drained from the battery so the battery will work less time - for me the best results for the RGB led was 15K)
  • some wire for the coils that has to be made on the toroid
  • for the RGB changing color LED version you may need also (not always, only if you are having problems with changing colors smothly) additional diode like 1n4148 or so and condensator about 1uF
    For the Jolie thief (how to) please refer to ready projects available over the internet and make some soldering.

How to use with any THING that you would like to make light of it .
It's simple and you don't have to make any projecting. Simply use your slicer.
I used Slic3r Prusa edition, here is what you have to do:

1. Pick your model and prepare it like you always do (resize etc), you have to remember that it should be empty inside, so no infill, also less perimeters = better light.
2. align it center
3. add "screw" file and align it wherever you want (suggest on the center also)
4. pick the first model and add a modifier (has to be aligned with the screw => cylinder -> radius 10 -> height 10 and add to features to modificator like 0 - perimeters, 0 - top bottom perimeters, 0 infil (if needed)
5. Slice it (check if it's ok and print).
6. Tealight should fit no problem.
   Some models doesn't need the screw implanted into the model, but the screw can help to be used as a stand - suggest to print screw standalone also.

This tealight uses jolie thief and may utilise bateries that are not working anymore in other devices as jolie thief can drain the baterries very low.
You will have a use for most of the old bateries instead of throwing them off :-)

Here are some designs that I used my tealight with (you can see them on the photos):

https://www.thingiverse.com/thing:75582
https://www.thingiverse.com/thing:1864269
https://www.thingiverse.com/thing:193814
https://www.thingiverse.com/thing:2025373
https://www.thingiverse.com/thing:19104
https://www.thingiverse.com/thing:1652279

UPDATES:
25.12.2018 - added screw for sphere like items