To calculate the average time between lessons for each student and rank the results in ascending order, you can use the following SQL query in PostgreSQL:

sql
SELECT student_id, AVG(time_between_lessons) AS average_time_between_lessons
FROM (
  SELECT student_id, 
         EXTRACT(EPOCH FROM (next_lesson - current_lesson)) / 60 AS time_between_lessons
  FROM (
    SELECT student_id, 
           lag(lesson_time) OVER (PARTITION BY student_id ORDER BY lesson_time) AS current_lesson,
           lesson_time AS next_lesson
    FROM lessons
  ) AS subquery
) AS subquery2
GROUP BY student_id
ORDER BY average_time_between_lessons;

The query first uses a subquery to calculate the time between consecutive lessons for each student. It uses the `lag` window function to retrieve the previous lesson time for each lesson. Then, it calculates the time difference between the current lesson and the next lesson using `EXTRACT` and `EPOCH` functions, and converts it to minutes. In the outer query, we calculate the average time between lessons for each student by taking the average of the time_between_lessons values. We group the results by student_id and sort them in ascending order by the average_time_between_lessons. You will need to replace `lessons` with the actual name of your table containing the lesson data. The table should have the columns `student_id` and `lesson_time`, where `student_id` is the student's identifier and `lesson_time` is the timestamp of the lesson. The result of the query will be a list of student_ids and their corresponding average times between lessons, sorted in ascending order.