Indeed, these diagrams are misleading to the beginners. I was asking exactly the same questions (to myself) when I first encountered them on this page.

There are two points need to be explained:

1. the external lines in these figures are NOT the "external lines" in the terminology of a scattering process. These lines actually plays the same role of those appearing in a propagator, as shown in the following picture

Apparently, the lines in the above figure does not mean external scattering particles. So we understand the figures in your post are actually propagators (1PI as you know), they will finally appear in the internal parts of a full scattering process.

2. The classical fields are suppressed in the figures. For instance, the $\lambda$ is a 4-vertices interaction, while in the second figure, it looks like a cubic interaction, what is wrong? The reason is that, the authors suppressed the classical fields. If you take it rigorously, you should have a figure like this.

Indeed, these diagrams are misleading to the beginners. I was asking exactly the same questions (to myself) when I first encountered them on this page.

There are two points need to be explained:

1. the external lines in these figures are NOT the "external lines" in the terminology of a scattering process. These lines actually play the same role of those appearing in a propagator, as shown in the following picture

Apparently, the lines in the above figure do not mean external scattering particles. So we understand the figures in your post are actually propagators (1PI as you know), they will finally appear in the internal parts of a full scattering process.

2. The classical fields are suppressed in the figures. For instance, the $\lambda$ is a 4-vertices interaction, while in the second figure, it looks like a cubic interaction, what is wrong? The reason is that, the authors suppressed the classical fields. If you take it rigorously, you should have a figure like this.