The only accurate statement among the three is Statement I. The presence of a lease rate indeed reduces the forward price of a commodity. A lease rate is essentially the return earned by the owner of a commodity when they lease it out. When a lease rate is present, it implies that the commodity can generate income, which reduces the need for the owner to sell the commodity in the future. This, in turn, reduces the forward price of the commodity. Therefore, the analyst's conclusion in Statement I is correct.

Statement II is incorrect. The forward price of a commodity actually decreases in the presence of a convenience yield, not increases. The convenience yield represents the benefit of holding the physical commodity (e.g., ability to meet unexpected demand), which effectively lowers the cost of carry and therefore lowers the forward price relative to what it would otherwise be.

Statement III is incorrect. As per the cost-of-carry model, an increase in storage costs leads to an increase in forward prices, not a decrease. Storage costs are a positive component of the cost of carry: $F = S \cdot e^{(r + u - l - y)T}$, where $u$ represents storage costs and $y$ represents convenience yield. Higher storage costs raise the forward price.