$(0, 1/3, 2/3)$ works as a strategy that strictly dominated $L$.
To prove that there are infinitely many of them:
Let $A_n=(0,1/2+\epsilon_n,1/2-\epsilon_n)$ where $\epsilon_n=1/n$ for $n=1,2,3,...$. We can see that for $n > 10$, $A_n$ strictly dominates L. So, since $n$ diverges, there are infinitely many $n$ for which $A_n$ is a strictly dominant strategy.
I chose $n> 10$ since $2<2.5-5\epsilon_n \Leftrightarrow 0,1> \epsilon_n$ and $1/n<0,1$ for $n>10$. The other inequalities don't require $\epsilon_n$ to be restricted.
Would this be a correct way to prove this?