Is the Lateran Baptistery really spolia?

and refurbished by the Barberini Pope:

and definitely so at the back:

and here:

Itg is not surprising that we find spolia incorporated here because, just acrfoss the road at the hospital, there survives part of a splendid late-antique portico:

S Lorenzo in Lucina narthex;

Throne in

Interest in mediaeval Cosmati work perhaps shown in: