Should Henry have handled his meeting with Lucy any differently? How so?

Henry is the maintenance manager at an older hotel that has been renovated in recent years. He is a newcomer to the property and just reached his six-month anniversary. Lucy is his administrative assistant. She supports him and the entire three-shift operation by entering and updating work orders on a computerized maintenance management system. She has been with the property for seven years and has performed well through a few organizational changes.
The department workload has been particularly heavy since the new wing opened in September. Around the beginning of October, Henry noticed that Lucy sometimes arrived back late from lunch breaks. It is now late October. Last week, Lucy started to fall behind in her paperwork. On Tuesday and Wednesday she arrived late and took long lunches. She called in sick on Friday and again this past Monday.