These screenshots are all taken at about 40,000Ls from the nearest star or other body, a few seconds apart, with a maximum non-SCO speed possible of around 500c and no in-system objects targeted.
There's two sets of lines visible in three of them, and only one in the fourth (at an intermediate speed). In all four the ship is travelling well below the current gravity well limit.
(Yes, you won't see two sets if you get clear enough of all stars to go at 2001c, but that's just because of where the cutoffs between the sets are; you stop seeing any but the shortest lines at a lot less than 2001c)
And conversely, here's one where I'm definitely being affected by a gravity well after just coming out of SCO not far from the star ... but there's only one set of lines, because my speed is again between the thresholds at which either the "faster" or "slower" set of lines would be appearing.
If you take two screenshots where you're travelling at identical speeds, but one of them is near a gravity well and one of them isn't, you'll see exactly the same parallax lines on both.
(Yes, if you're being affected by a gravity well, you'll see changes in the lines, because the gravity well will be changing your speed. Doesn't tell you at all whether your speed is 10% or 1000% of the maximum normal speed allowed by the current gravity well, though)