Lake Askja is a 11 sq kilometers and one of the deepest lakes in Iceland. You will see the beautiful Viti volcano with has beautiful geothermal water - you can bathe there as well but don't expect the water to be as warm as many of the natural hot pools.
Going to Askja is a full day adventure! Be sure you have a full tank of gas and some provisions. The drive alone is 6 - 7 hours roundtrip and therefore should only be included in your itinerary if you have the time and the weather is good enough to fully enjoy the scenery. The best and easiest route from the Ring Road is 901 to F905 to F910 to Dreki hut. Check-in with the staff at Dreki to determine road and trail conditions to Askja and if all sounds good, continue on F894 all the way to the parking area here. Though more direct, taking F88 is not recommended due to a large and challenging river crossing.
Since you will be driving on F-Roads it is important to know that a 4x4 vehicle is REQUIRED. F-Roads are only open in summer, sometimes not even until July. Check the road conditions and closures at road.is before you travel. There are no large river crossings to get to Askja as long as you are only driving on 901, F905, F910 and F894. However, there are some smaller and medium river crossings so please be careful and make sure you have experience crossing rivers. Do not take excessive risk. Not all car companies cover damage to cars in river-crossings and it can be easy to get stuck. In addition, not all 4x4s have the same capability for water crossings.
If you want to play it safe and be in a well-equipped, photogenic car, then you should rent an old-school Land Rover Defender from www.isak.is equipped with a snorkel. This helps ensure you don't drown the engine while crossing a river. Use the code "gunnar" for renting your Defender on a special price.
Tips on river crossings: https://epiciceland.net/icelandic-rivers-how-to-cross/. Make sure to go with the stream (diagonal across the river in the direction of the flow). Do not drive against the stream, but let the flow of the river help you cross.