Door lintel broken - replace door frame / lintel or harmless?

I believe that the brick is broken is not even the big problem. The question is why it broke and whether it will happen again or get worse?

these lintels are prestressed brick reinforced concrete lintels, the concrete core has one/two prestressed reinforcement bars inside, and is concreted into brick U-stones. The lintels are not as stable as solid concrete lintels, therefore they bend when overlaid without support. The shown chipping is obviously not so severe

The standard response is likely to be: "the plasterer does that"

You don’t break a door lintel that easily, not even deliberately.

Why plasterers? that just covers the frame

That looks like botched work overall. Note, for example, the cross joint in the masonry bond.

Note, for example, the cross joint in the masonry bond.

Some people are such good botchers, they could easily train botch specialists.