Thanks Rolando, but that's not worked. All the pen options were checked, originally. I have tried unchecking the 3 you mention above, one at a time, then in pairs, then all three, but this has not solved the problem.
Here is the sequence:
Open Onenote 2016 on a note. Select the Draw ribbon. On the ribbon, 'Type' is selected, 'Lasso Select' is not selected.
Approach the screen with the pen. When it's about 5mm from the screen, 'Type' automatically deselects (I guess this is 'Automatically switch between inking...' working). Write some handwriting on the screen. Tap Lasso Select on the ribbon. It is selected.
Use the pen, and it's working in Lasso mode.
Tap Lasso Select again on the ribbon. It becomes deselected, and 'Type' becomes automatically selected.
Approach the screen with the pen. At about 5mm from the screen 'Type' automatically deselects again
but Lasso Select automatically selects. I cannot find how to stop this automatic selection of Lasso Select when the pen approaches the screen, once it has been used.
I have tried the other, non-Office, version of OneNote as well and the same thing happens - once Lasso Select has been selected, you cannot go back to the state where neither Type nor Lasso Select are selected.