I just did this. The lever is splined and attaches to a splined shaft. It had corroded and was badly stuck.
Ultimately I purchased this puller specifically for the purpose of getting it apart:
https://www.mcmaster.com/6169K32/
I replaced the hollow center bolt in the
engine control with a solid one and loosened it one turn, then applied the puller. It took a great deal of force and I was afraid I was going to break something, but I did get the handle off in one piece. I fussed around
cleaning and greasing the
engine control, but ultimately was unable to get it to
work smoothly. I have a replacement on order.
The puller barely fit. I had to cut apart the plastic washer between the handle and the plastic housing to make room.
Hope this helps. Good luck.