Khizr Khan established the Sayyid dynasty. The Sayyids were of Arab descent and claimed to be descendants of Prophet Muhammad. Khizr Khan served as the governor of Multan under the Tughlaq dynasty and later established an independent kingdom in Delhi in 1414 CE. He ruled as the founder of the Sayyid dynasty until his death in 1421 CE.

The Lodhis, on the other hand, succeeded the Sayyid dynasty. They were of Afghan descent and were established by Bahlul Khan Lodi in the late 15th century CE. The Rajputs were a powerful Hindu ruling class in medieval India and did not establish a dynasty named after them. Lastly, the Khiljis ruled the Delhi Sultanate before the Sayyids, but they were not started by Khizr Khan.

In conclusion, the correct answer is Option 1 - The Sayyids.