Can a Trader Be Liquidated Based on Mark Price but Still Have a Positive P&L Based on Last Traded Price?

Yes, this is possible. If the Last Traded Price is temporarily much higher (for a long position) or lower (for a short position) than the Mark Price due to a short-term market anomaly or 'wick', the trader's unrealized P&L based on the Mark Price could be negative enough to trigger liquidation.

The Mark Price, being an average, is less volatile and is the true trigger for margin calculations, protecting against such temporary price spikes.