In the VFB:
-If you click the "Save" button in the upper left corner, this will save only your currently visible render element in the format of your choice (so if you select beauty and click "Save", it will save only the beauty pass, without any other elements such as the lightmix, even in the CXR format)
-If you click and hold on the "Save" button and select "Save all, this will save each separate render element as a separate file (of any format you choose)
-If you click and hold on the "Save" button and select "Save CXR", this will store all the information from the VFB (all render elements, including the LightMix) inside a single CXR file <--- this is the option you need
Alternatively, you can click "Save CXR..." in Render Setup > Scene.
I am guessing that when it did not work, you just pressed the "Save" button.
I will see if this could be improved so that clicking "Save" would always save LightMix and other elements, but not really sure about it.