This is how I understand it:
If the clamping force for a TC lockup clutch diminishes across it's life (usually due to TC clutch wear,) eventually there is insufficient clamping force to maintain static friction (lockup), and it will slip under acceleration/load. After it breaks static friction, the torque converter begins spinning differential speed and acting as a fluid coupling again, gradually taking load as it increases in differential speed. Once the TC starts bearing this load, the lockup clutch (which never disengaged any clamping force) eventually has sufficient force to regain static friction. Once it regains static friction, the TC slows to a stop, eventually putting full load on the clutch, and the cycle starts all over again. This cycle happens in fractions of a second, and feels like a vibration to the driver. Some software in ATs will recognize stick-slip shudder and disengage the lockup clutch for a duration, then reengage, just in case it was anomalous (ie, not due to insufficient clamping force) and to protect against clutch glazing and wear.