Derivatives of LiDAR are only as good as the point cloud itself. If buildings are left in the point cloud when first derivatives (DEMs) are created, the elevation values will reflect the heights of buildings, as well as ground. This is useful if you are determining the elevation of building rooftops. Second derivatives (contour lines) created from a DEM with rooftops, again, will reflect the values of the rooftops.
Look at this presentation. It explains and visualizes the difference between bare earth and first return DEMs, as well as DEMs used to visualize rooftops.
If it is rooftop height, bridge height, etc that you are after, then these surface models are necessary. However, if you require bare earth values (for a flood analysis, line of sight, etc), then a bare earth DEM may be required.
All this said, if you want elevation contours of buildings, then what you have will work. Be warned that contours of vertical surfaces will be dense if you generate small contour intervals (such as 1 or 2 feet). With ArcMap you can use the Contour tool to generate contours from your DEMs. With 1 meter cells, you are able to create accurate contours down to 1 meter. You can do smaller intervals, but the interpolated values will not be as accurate.