How do I power a LCD Backlight inverter (got from a disasembled LCD screen)
You need the find the specs for that particular P/N. They are not universal.
You can buy CFL tubes from Digikey for $5 or so. 1.5mm or 2mm probably by x mm long.

For example here is a T-Y interface spec. click image to open PDF file.

That looks like this.