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Can you recommend an open source GIS tools for modeling the water impounded on the upstream side of a dam using LiDAR data?

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You could also consider using GRASS-GIS to import and process your LiDAR data. There is detailed information provided on the GRASS Wiki and an example of a DEM created and visualised included below.

In order to estimate the storage behind a dam, you might be able to use the GRASS GIS module r.lake. However, you may need to modify the program in order to model the height and location of the dam itself.

r.in.lidar

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You have a LiDAR derived surface model and you want to calculate the volume of water that would be behind a theoretical dam? If so, have a look at this link http://www.bc-consult.com/tut/QGIS-volumes.php

If the dam is already in place and filled with water and you want to calculate that volume of water-you will need to collect bathymetry data.

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