For example some seeds (such as lentil seeds) require humid environment and washing ~2 times a day to sprout. How can I get a small portion of sprouts every day, with minimum attention (I'm not around most of the day)?
If you take a jam jar and fill it with enough seeds for 2-3 days, you can then rinse them thoroughly in water and drain it. The next day you can rinse it again and turn the jar upside down over damp kitchen paper. 1-2 days later you should have your sprouts.
You can then stagger this with another 2 jars so that you keep around a weeks supply.
This method takes about 20 minutes daily, if it's worth that to you. You can line a small tupperware container (or any other small container with a lid) with cheesecloth or similar. Each day, start a new one, with the desired amount of seeds for your needs.
Twice a day, take them to the sink, open the containers (individually of course), and lift out the contents in the cheesecloth by the 4 corners, for rinsing. Rinse the container too. Then place them inside with just enough water that they remain damp, and replace the lid.
You can do this in the morning and evening (handy if you work during the day), and have them sit on a counter (for green sprouts) or in the dark, like under the sink (for blanched sprouts).
To streamline the system, you could invest in making or buying pouches of similar light material as cheesecloth. this will make lifting the seeds/sprouts easier, and also the transportation.