I see all kinds of Workers taking Water from nearby Lakes, despite Wells being quite close to their home, both Workers close to and far from their home when they want to stock their Shelter with water. Their current distance to Water may make the Lake preferred, but the Well next door is not much further as they have to walk home to deliver it anyways, so a Well should receive have a higher priority - preferably the Well(s) that increases desirability for their Shelter should be auto-assigned to a Shelter by default.
All Wells are perfectly full of Water, Villagers just randomly prefer a Lake and then end up getting sick without a real way to prevent it other than perhaps walling off the Lake.