Sorry to hear this. Sounds like someone didn't think it through when they built that. I am in construction and have been sitting here thinking of a an easy cheap way to fix this. There really isn't one and it's hard to say without seeing it.
A grade change would work but very costly and a lot of work. Removing the lattice work and putting in gutters is another idea again a lot of work and somewhat costly. Is there a way to run metal flashing from the shingles down in between the 2X8's and sealing them up with caulk and possibly putting a gutter underneath the 2X8 framing. They should have at least put gutters up if not that a french drain in the pation would have worked well too.
Good Luck.
Dono
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