It's normal, at 2 years and over and the child will have to have their own seat, (usually at the cost of a standard ticket). The lap belt is considered safe enough. Parents may choose to purchase and use a child restraint system such as a CARES Harness if they consider it appropriate for their child, and nearly all airlines now allow them and can assist in fitting them.
Children under two years old are classed as an infant... they get a free ticket but they sit on a lap with an infant / extension belt.
It can differ slightly by airline but it's very commonly done this way.
I then thought - what do airlines do when one person turns up with two small children?
Those bookings aren't allowed, each infant must be accompanied by 1 adult.