LISP and overlapping address spaces
LISP does not solve the "problem" of overlapping subnets at multiple sites. For all of your LISP sites, you must ensure that IP addressing is unique.
However, in some scenarios, such as in a multi-tenant deployment where each tenant is responsible for their own IP addressing, there must be some provisioning for overlapping subnets. In this case, overlapping IP address spaces can be achieved by preserving the traffic separation beyond the fabric border and by employing NAT.
For information about a similar feature take a look at LISP host mobility use cases.