Hi Jay,
First of, welcome to NPN! Glad to have you here.
I think we can all sympathize with less than stellar conditions. In fact I was just with Steve a couple weeks ago in Yosemtie and he can attest to 3+ days of drizzly overcast. So there’s two things to address. But first, I wanted to comment on your posted image! I think you did very well in the flat light. I like the perspective and how you framed the lighthouse over the lovely and colorful flowers. This is very nicely framed image. The color, saturation and processing in general for the flowers/vegetation looks great.
For any tips, both Steve and Michael have already chimed in with great advice. I can only add on to it. They address the two different aspects. One, is how best to photograph at the time when you don’t have a choice of conditions, and second, what can you do after the fact.
In the first case, I actually prefer overcast light for most situations mostly because colors don’t get washed out, you don’t have to worry about hot spots and you can photograph things you might not normally be able to do because of hot light on bluebird sky days. I embrace these conditions also because contrast is greatly reduced. To be sure it’s easier to process and ADD contrast in Post, than it is to deal with high dynamic range, high contrast of photos taken in harshr light. And let’s face it, when your opportunities are when out traveling or visiting places with family or friends, it’s not likely you’re there during the sweet light hours around sunrise or sunset - so you’re dealing with flat or harsh light regardless.
Anyway, my big tip in these flat light - cloudy, boring skies… is minimize including the sky, if not entirely! Even in post after the fact and with your particular image, I could see a significant crop to remove much of the sky (and still give the lighthouse some room); So I’ll echo Michael’s thoughts and simply look for things where colors are enhanced and look great, or as I mentioned, just try and limit the flat sky all together.
In post, the second aspect, I do similar as Steve, only I don’t use LR, I do a similar thing in ACR, Adobe Camera Raw (actually the same processing engine anyway.) Select/mask the sky and adjust withe various sliders. One tip, and I’m assuming is also available in LR, is by pressing the “ALT” key (in Windows, is it the Option key in Mac?) while you’re making adjustments using sliders. With highlights, whites, exposure sliders, you can see when the values exceed their limits and wash out or black out. I think more difficult for me to describe… sorry!
Thanks for sharing, hope this helps.