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First, we need to determine the elements of the relation R. The relation is defined by $xRy$ if and only if $y = \max\{x, 1\}$.
For $x = -2$, $y = \max\{-2, 1\} = 1$. So, $(-2, 1) \in R$.
For $x = -1$, $y = \max\{-1, 1\} = 1$. So, $(-1, 1) \in R$.
For $x = 0$, $y = \max\{0, 1\} = 1$. So, $(0, 1) \in R$.
For $x = 1$, $y = \max\{1, 1\} = 1$. So, $(1, 1) \in R$.
For $x = 2$, $y = \max\{2, 1\} = 2$. So, $(2, 2) \in R$.
For $x = 3$, $y = \max\{3, 1\} = 3$. So, $(3, 3) \in R$.
Therefore, $R = \{(-2, 1), (-1, 1), (0, 1), (1, 1), (2, 2), (3, 3)\}$. The number of elements in R is $l = 6$.
Next, we need to find the minimum number of elements to add to R to make it reflexive. A relation is reflexive if $(x, x) \in R$ for all $x \in A$. The set $A = \{-2, -1, 0, 1, 2, 3\}$. The elements $(x, x)$ that are not in R are $(-2, -2), (-1, -1), (0, 0), (1, 1)$. Since $(1,1), (2,2), (3,3)$ are already in R, we need to add $(-2, -2), (-1, -1), (0, 0)$ to make R reflexive. Thus, $m = 3$.
Now, we need to find the minimum number of elements to add to R to make it symmetric. A relation is symmetric if whenever $(x, y) \in R$, then $(y, x) \in R$. The current relation is $R = \{(-2, 1), (-1, 1), (0, 1), (1, 1), (2, 2), (3, 3)\}$.
For $(-2, 1) \in R$, we need to add $(1, -2)$.
For $(-1, 1) \in R$, we need to add $(1, -1)$.
For $(0, 1) \in R$, we need to add $(1, 0)$.
For $(1, 1) \in R$, we don't need to add anything.
For $(2, 2) \in R$, we don't need to add anything.
For $(3, 3) \in R$, we don't need to add anything.
So, we need to add $(1, -2), (1, -1), (1, 0)$. Thus, $n = 3$.
Finally, we need to find $l + m + n = 6 + 3 + 3 = 12$.
Correct Answer: 12