Home DVDs converted to MKV - lines on video during playback

Not so much that you could notice - for DVDs it’s very likely, if you use the right magic tricks your encode will look better than the source - it sure won’t be interlaced and that would be a step in the right direction:

HD Above - 480p Below.
De-Interlace is in Filters/De-interlace/No Detection/Yadif - Default/Lapsharp/Light/Film (probably, but pick Animation if necessary - like if you’re encoding animations).

More than about 2500Kbps is a waste of time (for DVDs/Standard Rez), but do a 2 pass at whatever you decide on.

BTW - there should be a setting in that recording device (are these from a camera recorder?) to disable interlacing. There is no earthly reason to have it on - if you have a choice.