Yes, they can. Since three points define a plane, take any two points on one line and a point on the other line, and form the plane with those three points. Once you have that, then use Euclid's test to see if they are parallel. Alternately, if the planes themselves are parallel, then the lines are as well, since they definitely will never intersect.
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Skew Lines. :)
skew lines
Parallel lines would always lie in the same plane. They would need to be skew lines.
Skew lines are lines that lie on separate planes. and do not intercept parallel lines that are sometimes on the same plane, but don't intersect
They are skew lines. Two parallel lines must be in the same plane.