I'm going to guess that the figures in your question are percents. After lunch he cuts 34% of the 23% he has left (If I'm reading the question correctly). "Of" usually means to multiply. In this case .34 times .23 equals .0782, or a little under 8%. He cut a little under 8% of the lawn after lunch.
The correct form of invitation in "you are invited to lunch" or "you are invited at lunch" is "you are invited to lunch". You could also say, "you are invited to lunch at my house" as this would be grammatically correct.