<p>In my Direct3D application, the camera can be moved using the mouse or arrow keys. But if I hard code (0,1,0) as the up direction vector in <code>LookAtLH</code>, the frame goes blank at some orientations of the camera.</p>

<p>I just learned the hard way that when looking along the Y-axis, (0,1,0) no longer works as the Up direction (seems obvious?). I am thinking of switching my up direction to something else for each of these special cases. Is there a more graceful way to handle this?</p>

Assuming you can calculate a vector pointing forward (what you are looking at - your position) and a vector pointing right (always on the XZ-plane unless you can roll). Normalize both these vectors, then up is forward x right (where x is cross product).
In general, you can plug in your yaw, pitch and roll into a rotation matrix and rotate the axis vectors to get right, up and forward, but I guess that's what you are using LookAtLH to avoid.
See
http://en.wikipedia.org/wiki/Rotation_matrix#The_3-dimensional_rotation_matricies