I feel like I already know the answer to this question, but was hoping to get clarification.  The ability to change the Today's Tasks view on the home page and make it sticky doesn't exist, correct?  The default view is for "Today", but in Classic a user can choose different options and each time they login it'll show that option.  In Lightning, if I change that view to "My Tasks" to see everything, it reverts back to "Today" when I login or refresh the home page.  This seems like common sense to have as a function, but it doesn't appear it's there.  If it's not, I feel like it's another miss by Salesforce when it comes to Lightning.  For all the cool features it has, there are so many little things that a user can do in Classic but they can't in Lightning...