Wash the rhubarb and trim the ends. Peel if desired. Cut into small pieces and place in a large enough pot.
Add both types of sugar, cinnamon stick, and lemon juice. Mix well and let the rhubarb steep for 20 minutes, creating a flavorful rhubarb juice.
Place the pot on the stove and add the juice. Bring to a boil and simmer for 7 to 10 minutes.
Remove from heat and let it sit in the pot for an hour. It is ready for use by then.
If you want to preserve your compote, prepare the jars and ensure they're clean. Boil the rhubarb compote again and pour it into the jars while it's still hot. For a good seal, it's important that the jars cool down as quickly as possible. Place the jars halfway into cold water or in a cool place like the basement.
Notes
If you're using relatively thick rhubarb and not peeling it, pre-boil the pieces in water for a few minutes to reduce the oxalic acid content. Then discard the water and add the remaining ingredients, simmering until you have a compote.