In the mechanic's lien context, the mechanic services your car thereby adding value. That value-added serves as the basis for the mechanic's security interest in your car. That security interest (the lien) is the consideration you give (meaning, payment) to the mechanic in exchange for his services. That lien is "extinguished" upon payment of your debt obligation to the mechanic.
The HOA functions in almost exactly the same way. While the HOA may or may not perform repairs (in some condominums, HOAs are responsible for certain repairs), the HOA nevertheless provides certain and definite value-add services to your home (security, pool, parks, open-areas, community centers, trails, etc...). Like the mechanic's lien, the HOA develops its own security interest in your home to secure payment from you because you have received the benefit of the value-add services provided by the HOA. That security interest is extinguished/satisfied upon your payment of dues.
They function almost identically. For purposes of this discussion, the claim that HOAs don't provide repair services is spurrious and irrelevant.