I thought we had explained. The light weight batteries need a different charger, which makes it a bit more complex. I can be done but.....
Some Car battery sized 12V batteries come with the BMS built in and are a direct replacement. The high energy density of the Li?? batteries mean there is room in the same sized battery case to fit the electronics.
To diy you need to ensure that power to the Twizy comes directly form the Battery ie. big Diode in line. While the power from the Twizy to the battery goes via a new charger. There are 12V to 12V Lithium battery charges that would do this job. Not cheap in comparison with a straight swap. As the Twizy 12V battery is small by the time you have added the extra charging circuit you may not save any weight
Remove weight else where ie. remove the charging cable - making it detachable like the big EV's. Empty the windscreen washer bottle, at least reduce it's size. Take the speaker cowling out and speaker supports., Room the glove box lids. Any of which will save more weight that the battery swap.