Also, it does NOT have big rhizome roots.

Perhaps Dianella tasmanica 'Variegata'? Just a guess based on a recent visit to Florida where these were very popular outdoor plants.

Dianella grows like a grass, not in fans like an iris. This looks like it could be a variegated form of Japanese wood iris, Iris japonica (aka orchid iris). A stubby, mostly evergreen species that produces sprays of very fetching orchid-like flowers.

Here is a link that might be useful: Iris japonica 'Variegata'

I agree it isn't Dianella, but I am intrigued by the OP saying it doesn't have a rhizome. Both Dianella and Iris japonica do and AFAIK, all the fan iris do as well

Neomarica gracilis variegata?

OP said no "big rhizome roots - I assume that means rhizomes similar to the Iris pallida or other bearded forms. Iris japonica has what I would consider to be enlarged, fleshy spreading roots - more like Siberian and other bearded iris - rather than the fat, exposed rhizomes of the germanicas.

The solution would be to wait until it bloomed - one would know for sure then :-)

Hi All,
I got an ID elsewhere. Sisyrinchium striatum 'Variegatum'
Remy

Has it bloomed yet? That would confirm.