I am not sure its possible to project a basemap from AGOL, but you can try turning if off when you open a new project then bring in your LAS first, save the project, then add the basemap if you want it to be in your map. ArcGIS Pro should honor the first layer added to the project as the default projection. To do this go into your ArcGIS Pro options by Open ArcGIS Pro, click on the Projects tab, then choose "Options" from the left hand column list. When the options dialogue appears, click on "Map and Scene" then click the down arrow for the "Basemap" and check the radio button for "None" and click "OK". Restart ArcGIS Pro, add your LAS file to a new map and save it. Your LAS should be the default projection for your project and anything else you choose to add ie. basemaps or other layers, they should re-project on the fly. If this doesn't work let me know and I can provide another solution.
Amanda Bishop, GISP