Joseph's lunch at a restaurant costs $13.00, without tax. He leaves the waiter a tip of 17% of the cost of the lunch, without tax. What is the total cost of the lunch, including the tip, without tax?

To calculate the total cost of Joseph's lunch including the tip, we start with the cost of the lunch and then calculate the tip based on that cost.

1. Cost of the lunch: $13.00
2. Tip percentage: 17%

We first need to calculate the tip:

\[ \text{Tip} = \text{Cost of lunch} \times \frac{\text{Tip percentage}}{100} \]

Substituting in the known values:

\[ \text{Tip} = 13.00 \times \frac{17}{100} = 13.00 \times 0.17 = 2.21 \]

Now, we add the tip to the cost of the lunch to find the total cost:

\[ \text{Total cost} = \text{Cost of lunch} + \text{Tip} = 13.00 + 2.21 = 15.21 \]

Thus, the total cost of the lunch, including the tip, is:

\[ \boxed{15.21} \]