Thanks Zhouyi. This works - although I had to make some modifications! It's a smart solution to create the measure "Current Month Sales" and not put Order Date as the filter.
For those of you who are looking for an answer, please note that the measure "last 3 month Avg" uses FIXED DATETRUNC('month', [Order Date]). IF you have other dimensions on the filter shelf, those dimensions won't be used as filter due to the FIXED statement, and therefore, the number shown will be incorrect.
For me, as I only have one value each month, I just added the AVG formula directly to the "last 3-month Total" measure to get the results I am looking for.