The instructions for deploying an HPC Cluster (e.g. step 1.5 on this page in TechNet) are very clear that HPC cluster nodes "must be members of an Active Directory domain".
Does the Active Directory Lightweight Directory Services provide this?
That is, can the HPC cluster use AD LDS for its Active Directory domain, or do I need the full AD DS (Domain Services) role?
No, AD LDS does not have the concept of member servers or computers joining a domain. It's just an LDAP front-end.
You need Active Directory Domain Services.