Bleiler--Litherland's lower bound conjecture for hyperbolic lens space surgeries

Let $K\subset S^3$ be a hyperbolic knot, and suppose that a surgery on $K$ yields a lens space of order $r$. Bleiler--Litherland's conjecture. The order satisfies

$$r\geq 18.$$

The paper proves that a hyperbolic knot with a lens space surgery has order $r=14$ or $r\geq18$, so the conjecture amounts to excluding the remaining order-$14$ case. The source gives no resolution of that case.