Pruning questions: fortnight lily and lavendar

Immediately after blooming, cut the top third of the stem off. (The part with the grey leaves, not to be confused with the flower stalk)

Fortnight lilies (Dietes iridiodes, also known as D. vegeta) are evergreen and should not be cut back. The flower stalks will rebloom if left alone. Removing them can prevent flowering for a season. Only remove the stalks if they are obviously dead, and cut back only dead portions.

Yes, removing spent flowers will promote new growth and (later) more flowering. However, when cutting, always leave a few green leaves. If you cut below the lowest green leaf, the stem will die.