[@Wojciech Różański ] I just heard back from the team that "cross-tenant calls are not supported for the feature as of now". Therefore, it is not possible for a user delegated through Azure Lighthouse to be able to view the compliance reason.
The "feature" in my reply above means the "ability to check the non-compliance reason OR policy evaluation details". The user delegated to "reader" role through Lighthouse can view the compliance state of resource (compliant or non-compliant) in the Policy's compliance view. However, further calls from this user (from a different tenant) to get the details of non-compliant reason (policy evaluation details) are not supported, causing the error message as seen in this case.
I would request submitting it as an idea on the feedback portal for Azure Governance for it to be considered in future.