I do attend Daily Mass and for the last few decades a lay person has always read the readings for the day. In fact, the only time in my recent memory that the priest has done so was a couple of years ago when we were in the midst of a terrible snow storm and only myself and one other parishoner showed up for Mass. Even so, the priest did ask me before Mass if I would do the readings but I had laryngitis and the other parishoner was actually a member of the Korean community of our parish and did not read English well at all.
At all parishes that I am familiar with, there will be a list of people who volunteer to do the daily readings. Usually, the parish secretary will check with those people in advance of each week to make sure that they will be available on the day to which they are assigned. My parish tries to have two people available for each day (with one the actual assignee) just in case unforeseen circumstances occur and the assigned reader doesn’t make it to Mass.