Yes, you could use the term lexical order here. Usually, if one has a well-ordered list of orders $P_\alpha$, then one may define the lexical order on the product of the underlying space by placing $\vec x$ before $\vec y$ if the first difference $x_\alpha$ is before $y_\alpha$ in $P_\alpha$. In your case, you don't have orders, but merely pre-orders (since two sheep could have the same age, etc.).
But in your case, you don't want the product space, since you want to order the individual sheep, not sequences of sheep. All your orders have the same underlying set (the set of sheep), and so this isn't the usual meaning of the lexical order. One way to think about it is that you are restricting the lexical order to the constant sequences.
If $P_\alpha$ is a well-ordered seqeunce of pre-orders on a set $X$, we may define the order on $X$ by placing $x$ before $y$ if the least $\alpha$ where they are not equivalent has $x$ before $y$ in $P_\alpha$.
It is important that the set of orders is well-ordered, since otherwise there may be no such least difference coordinate $\alpha$, and the idea will run aground.