IGI stands for the International Gemological Institute — one of the labs that grades diamonds against the 4Cs: cut, colour, clarity and carat.
It doesn't matter whether the diamond is mined or grown. Same lab, same scale, same scrutiny.
Every E'LHAA diamond over a carat is IGI certified, and the certificate travels with the piece — not as an add-on, just as part of what you're buying.
If you ever want a diamond independently checked, the certificate number is what an appraiser will ask for. Keep it somewhere safe.