Full sun to mostly sun, regular water. It might germinate with no chill, but a month or so of cold moist can improve germination so makes a good winter sowing candidate. I've had Sisyrinchium striatum (many self sown seedlings with this one), and Sisyrinchium angustifolium but not the angustifolium 'Lucerne' that you mention. In looking for what you bought, I find suggestions that one does not self sow to the extent the others do, to notes that it is sparse in seed set, and a couple of sources that say it is outright sterile.

Seed pods if you have them are not large but clearly visible -

Here is a link that might be useful: {{gwi:390151}}