Hi Nicky,
With the approval of your doctor, I think your insurer will consider approving a brief, emergency visit outside Canada to visit your sister who is gravely ill. You do need to get the approval of your insurer in advance of travel plans as it is unlikely that your LTD plan allows travel outside Canada, and possibly the US, without approval. A three month out-of-country trip might fall outside the definition of a “brief emergency visit.”
Did you think about out-of-country medical insurance for your trip? Even if you currently have coverage from your employer, it probably has a trip duration limitation (i.e. 30 day trip). In addition, regardless of the length of your trip, most out-of-country medical plans have a pre-existing medical condition exclusion (i.e. they will not pay any medical expenses for conditions related to a medical problem that existed before you departed on your trip). The pre-existing medical condition exclusion clause is this is something that everyone should consider before travelling, especially somebody who is currently so ill they can’t work (red flag for out-of-country medical insurer). Paying for medical treatment out of your own pocket while out of country can be catastrophic!