No, Lemmy servers are not exempt from GDPR compliance. The household exemption (you are not subject to gdpr for private activities) only applies for purely personnal activities. As soon as a service is offered to someone else, the exemption is no more applicable.
That's one of the drawback about open-source projects, they are designed to fulfill a need (persistent storage & decentralised communication for Lemmy), and no one give a f*ck about legalities.
It misses the most important information: why.
The CNIL (French privacy regulator) slapped Discord in October last year because they never deleted accounts (hi GDPR).
Since then, all tech companies are hurriedly designing a plan to mass delete inactive accounts.