I'm not sure I agree with your choice of title. Someone who chooses solitude at a beach for a break doesn't mean they're lonely.
I like the concept of the first one framing the scene with the building, the ocean and clouds on the horizon. I'm somewhat ambivalent the angle, as I suspect this might have played better if you were more straight on.
The second seems lacking in interest. Perhaps a tighter crop of the man, as he looks like he has an interesting face, and makes me curious to see what he's found.