There is no precise rule about grid resolution, but ideally you would like each grid cell to be representative of at least a single elevation value. In most cases with lidar data, the cell value is calculated from a few points. Points2Grid (P2G), the gridding software developed by OpenTopography, essentially assumes that grid resolution is greater than point spacing (i.e. a 1 m DEM can be created from 3 shot/m2 data density), and thus it is appropriate to perform a local operation on the points (e.g. take the mean values in a search area around the grid cell center). If your shot spacing is greater than the grid resolution, you will need to use a true interpolator like a spline or kriging to fit a surface to the points and to fill the holes. Take a look at this page and this page to learn more about how P2G works.
As a rule of thumb, to determine what grid resolution is supported by a given lidar point cloud density, take the square root of the point density per unit area (e.g., 5 pts/meter2). Point densities for each lidar dataset can be found below the "Overview" section. For example, if a dataset has a point density of 5 pts/meter2, then this dataset will roughly support approximately a 50 cm grid. (√(1/5) = 0.45). When extracting ground points only, users should assume a lower point density in the ground class, for example, 2 pts/meter2. In this case, the chosen grid resolution should be no smaller than 70 cm (√(1/2) = 0.7).
Note that for fairly dense data sets like the GeoEarthScope and B4 projects, you can reliably make DEMs at 0.25-0.5 m resolutions with 0.8-1 m search radii. The advantage of using the OpenTopography custom DEM functionality comes in the ability to simultaneously run a number of jobs using various search radii and grid resolutions. Once the jobs are complete, you can determine which DEM is optimal for your project's needs.