For a single container to hold multiple items, both container and contained are singular. A matchbox, a briefcase, a bookshelf, a notebook, a sock drawer.

Glasses case is widely used, maybe because glass case would be confusing. Some people are not comfortable with this usage snd say spectacle case instead.

The correct term is therefore

a contact lens case

For a single container to hold multiple items, both container and contained are singular. A matchbox, a briefcase, a bookshelf, a notebook, a sock drawer.

Glasses case is widely used, maybe because glass case would be confusing. Some people are not comfortable with this usage and say spectacle case instead.

The correct term is therefore

a contact lens case