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If you're drawing lines a lot and it's 100% performance critical (and it's lagging with the previous method) you'll probably need to write a shader to handle it. I haven't personally done this, but I'd assume you'd have a large texture and within the pixel shader you'd check the pixel's position against the line, and if the position is close enough then set the colour. Closest point to line, I know this looks scary, but it's quite simple actually, I have a raycaster in C++ which finds the closest point but in 3D here, for reference.
You can do all of that in MonoGame. For line drawing, might I interest you in my shape drawing library? https://github.com/Apostolique/Apos.Shapes.