RAA has an LSA Synopsis here
https://members.raa.asn.au/storage/lsa-synopsis.pdf
extract from that;
"The Special Certificate of Airworthiness for LSA is for production ready-to-fly aircraft. These aircraft may be used for hire, flying training and towing gliders. The Special Certificate of Airworthiness remains valid provided the aircraft is maintained in accordance with the requirements of the manufacturer and the aircraft has not been modified unless approved by the manufacturer. However, if the aircraft is not maintained in accordance with the manufacturer, or the manufacturer can no longer provide the continuing airworthiness, or the aircraft is modified without the manufacturer’s approval, the Special Certificate of Airworthiness will no longer be in force and the owner will need to apply for an Experimental Certificate to operate the aircraft"
Evektor Manual says motor to be maintained in accordance with the Rotax Maintenance manual.
Rotax maintenance manual lists TBO as 2000hrs or 15 years. Doesn't say anything about running on condition, so doesn't allow or specifically disallow, depends on your interpretation.
EDIT:
from the Rotax Maintenance Manual;
"GENERAL OVERHAUL (TBO)
Definition The time between overhauls (TBO) for all objects (such as the engine, component assemblies,
add-on components) is the approved length of operation under normal operating
conditions before it becomes mandatory to send in these objects for an overhaul.
Normal operating conditions are the conditions which comply with the manufacturer's and
the aviation authority’s recommendations for the certification of airworthiness."
They've used that word, mandatory, so to comply with the Special Certificate of Airworthiness for LSA, it is mandatory to overhaul the motor at TBO.