LAM Pro is licensed per installation. It is independent of who accesses the application and how many LDAP servers are managed.
Single machine license
If you install one LAM Pro installation on a single server then you need the single machine license.
This single installation can be used to manage an unlimited number of LDAP servers by configuring multiple LAM server profiles for this installation. In this case any LAM Pro user can see all server profiles. However, he may only login to his own profile by configuring LAM server profiles or using LDAP ACLs.
A company license allows unlimited LAM Pro installations on servers that belong to the same company.
E.g. if your company has four LDAP servers and you want to manage them by three independent LAM Pro installations then a company license would be the right solution.
Multiple single machine licenses
If you have multiple LAM Pro installations on different servers which belong to different companies (but may be managed by you) then you need multiple single machine licenses.
The servers may belong to subsidiaries of your company or customers (but may be managed by you). In this case you need one single machine license for each LAM Pro installation.
If you are a hosting provider then the company that rents the server is important. E.g. hosting two servers for two different companies requires two separate licenses.
Virtual servers count as physical servers.