Solution:

Suppose there are $n$ settlements $A_1, A_2, \ldots, A_n$ in counterclockwise order around the lake. We will use cyclic indices, so that $A_{n + 1}$ means $A_1$, and so on. WLOG $A_1$ has a direct service to $A_2$. Then it follows that $A_2$ does not have a direct service to $A_3$, so $A_3$ does have a direct service to $A_4$, and so on. So $A_i$ has direct service to $A_{i + 1}$ iff $i$ is odd. But $A_1 = A_{n + 1}$ has direct service to $A_2$, so $n$ must be even.

Now suppose we want to get from $A_i$ to $A_j$. If there is direct service we are done. So suppose not. Then there must be direct service from $A_{i + 1}$ to $A_{j + 1}$. If $i$ and $j$ are both odd, then there is direct service from $A_i$ to $A_{i + 1}$ and from $A_j$ to $A_{j + 1}$, so we can make the journey in 3 trips. If $i$ and $j$ are both even, then we can go $A_i$ to $A_{i - 1}$ to $A_{j - 1}$ to $A_j$. So suppose $i$ and $j$ have opposite parity. WLOG $i$ is odd and $j$ is even. If there is direct service from $A_i$ to $A_{j - 1}$, then we can make the journey in two trips: $A_i$ to $A_{j - 1}$ to $A_j$. If not, then we can go $A_i$ to $A_{i + 1}$ to $A_j$.