xlabel() and ylabel() take a string. So after the axes handle, you have to give a string, not the index of the selected drop down list. Presumably the string you want to show is in the drop down list. Here is how to get it:
selectedIndex = app.LeftYAxisDropDown.Value;
dropDownItems = app.LeftYAxisDropDown.String; % Get all drop down items into a cell array.
axisLabel = dropDownItems{dropDownItems};
ylabel(app.UIAxes, axisLabel)
selectedIndex = app.XAxisDropDown.Value;
dropDownItems = app.XAxisDropDown.String; % Get all drop down items into a cell array.
axisLabel = dropDownItems{dropDownItems};
xlabel(app.UIAxes, axisLabel)
