The verb "cambiar" is followed by a "de"-complement to indicate that the thing or person being substituted for belongs or belonged to (or was used by) the subject:
Cambié de coche. (I replaced my old car by a new one.)
Cambié de novia. (I replaced my old girlfriend by a new one.)
Cambié de look. (I replaced my old look by a new one.)
With "cambiar" alone, the concept of possession is absent, except when the verb is pronominal or a possessive is used, e.g. Se cambió el nombre / Cambió su nombre. (He/She changed his/her name.)
From a grammatical point of view, "cambiar de" is intransitive and can be pronominal, while "cambiar" is mainly transitive (the only case that comes to mind where "cambiar" is intransitive is when somebody says: Cambié -- meaning: I am a new person).
Concerning "cambiar de", RAE's dictionary says (the bolds are mine):
- tr. Dejar una cosa o situación para tomar otra. U. t. c. intr. y c. prnl. Cambiar DE nombre, lugar, destino, oficio, vestido, opinión, gusto, costumbre.
All the objects mentioned above have to be understood as linked with the subject by a relationship of possession if "de" is used:
- cambiar(se) de nombre: change your name
- cambiar(se) de lugar: change your seat
- cambiar de destino: change your destination
- cambiar(se) de oficio / trabajo / empresa: change your profession / job / the company you work for
- cambiar(se) de vestido: change your dress
- cambiar de opinión: change your opinion
- cambiar de gusto: change your likes
- cambiar de costumbre: change your habits
Using the example of the lamp, we could say:
- Como no funcionaba la bombilla, cambié de lámpara. (As the light bulb did not work, I moved to another lamp / I started using another lamp).
- Como no funcionaba la bombilla, cambié la lámpara. (As the light bulb did not work, I changed the lamp.)
The difference between (1) and (2) is that in (1) it is clear that the person was using the lamp that did not work. This lamp-user relationship is not present in (2), where the lamp is external, or unrelated to the person.