I think the problem comes when the lcp image is resized (because the transparency). Doing the composition in other way lets you have the nice image we all expect:
ImageResize[
ImageCompose[
GeoGraphics[{}, ImageSize -> 2000,
GeoRange -> {{-89, 89}, {-180, 180}}, GeoZoomLevel -> 2,
GeoProjection -> "Equirectangular"] // Image, lcp], 1000]
I tried first doing the resize over the lcp, but got the same bad result, so better do the composition first, then the resizing. I know this looks like a workaround, but the "GeoImage" way does perform something like the resize, so has the same artifacts as ImageResize[lcp, 1000].
