Is it possible to remove outlying elevation values from a LAS file?

No, it is not possible to remove elevation points from the LAS file. However, it is possible to classify the points as noise and filter the data out. Using the Classify LAS Noise tool in ArcGIS Pro to classify the points as noise, follow the steps below. 

Note:
The Classify LAS Noise tool requires a 3D Analyst license. For more information, refer to Classify LAS Noise.

1. Right-click the point feature (LAS) layer containing the noise > Properties.
2. Select LAS Filter in the left pane, uncheck the 7 Low Noise check box, and click OK.