It looks like you are using
R. If so, note that you can identify points on a scatterplot using ?identify. I think there are several things going on here. First, you have a very influential point on the plot of
LN_RT_vol_in ~ LN_AT_vol_in (the highlighted one) at about (.2, 1.5). This is very likely to be the standardized residual that's about -3.7. The effect of that point will be to flatten the regression line, tilting it more horizontal than the sharply upward line you otherwise would have gotten. An effect of that is that all your residuals will be rotated counterclockwise relative to where they would otherwise have been located within the
residual ~ predicted plot (at least when thinking in terms of that covariate and ignoring the other one).
Nonetheless, the apparent straight line of residuals that you see would still be there, as they exist somewhere in the 3-dimensional cloud of your original data. They may be hard to find in either of the marginal plots. You can use the identify() function to help, and you can also use the rgl package to create a dynamic 3D scatterplot that you can rotate freely with your mouse. However, note that the straight line residuals are all below 0 in their predicted value, and have below 0 residuals (i.e., they are below the fitted regression line); that gives you a big hint for where to look. Looking again at your plot of
LN_RT_vol_in ~ LN_AT_vol_in, I think I may see them. There is a fairly straight cluster of points running diagonally down and to the left from about (-.01, -1.00) at the lower edge of the cloud of points in that region. I suspect those are the points in question.
In other words, the residuals look that way because they are that way somewhere within the data space already. In essence, this is what @ttnphns is suggesting, but I don't think it's quite a constant in any of the original dimensions--it's a constant in a dimension at an angle to your original axes. I further agree with @MichaelChernick that this apparent straightness in the residual plot is probably harmless, but that your data are not really very normal. They are somewhat normal-ish, however, and you seem to have a decent number of data, so the CLT may cover you, but you may want to bootstrap just in case. Finally, I would worry that that 'outlier' is driving your results; a robust approach is probably merited.