Looks like chickweed.
hortster

I'd not suspect chickweed. In that area, looks like a mulched bed, a garden rake shuffled over the mulch will disrupt those plants roots enough to cause them to die.

Here is a link that might be useful: chickweed images

I see some violets, but the primary plants may be Impatiens pallida, jewelweed.

Did a soil test indicate there was a problem with the PH of your soil?

I see a chickweed (Stellaria sp.) and another seedling. Possibly Hairy Bittercress (Cardamine hirsuta)

I thought jewelweed, as well.

Just an FYI -- the pine needles/pine trees cause acid soil is just a myth. Pine trees tend to prefer slightly acidic soil, but there is no cause and effect. Always better to test your soil pH before adding lime -- not saying you didn't -- but throwing down lime without doing so can do more harm than good.

There isn't much you can do about the weeds now except preventing them from setting seed -- so I would keep them mowed low as soon as they start their flowering/seed production in late winter/early Spring (this is as soon as we break from the winter pattern and things warm just a little bit -- as early as late February depending on where you are, elevation, etc.).

I would wait until late summer/early fall to try to build the lawn (aside from a pre-emergent for summer annual weeds in Spring). The folks over on the lawn forum know a tremendous amount about how to establish a lawn that will choke out weeds. But, I will say that condition number one is you can't grow dense cool-season turfgrass without at least 5-8 hours of sun per day (and the 5 is pushing it).

Good luck!

Probably the main reason you have a patchy lawn is because of the massive pine tree
casting dense shade
limiting the amount of rain that reaches the ground
having a strong network of surface roots
distributing an annual load of cast needles, male cones, needle sheaths

If you haven't found the seed source for the flush of annuals (or young perennials) you are seeing in your yard then you will probably see more of them in spring. Particularly if you have wet spring weather in your area.

You may have to reconsider having a traditional lawn in your yard.

One thing you could do is to topdress the bare patches with some good weed-free compost for over the winter - just to get the soil life working again.