Lossy compression achieves its size reduction by throwing data away and not keeping a way back. The discarded information is chosen to be the information human vision is least likely to miss — fine colour detail, high-frequency texture, small differences between adjacent frames.
Every video codec in normal use is lossy. H.264, H.265, VP9, AV1 all are. So the phrase "compress without losing quality" is, taken literally, describing something that does not exist. What it describes in practice is compression whose losses you cannot see at normal viewing size and distance, and that is a genuine and achievable goal — because most video carries a lot of slack.
Phone recordings, screen captures and editor exports are routinely encoded well above what their content needs. Removing a large fraction of such a file changes nothing perceptible. Footage that has already been compressed hard has no slack left, and pushing it further shows immediately.
The practical test is whether you can tell the difference on the frames that are hardest to encode: faces, hair, gradients, water, grass, and anything moving fast. Those are where lossy compression fails first, and where a before-and-after comparison is worth making.
Two rules follow. Keep the original — the discarded data is not recoverable from the compressed copy. And compress once, because each additional lossy pass starts from the previous one's losses.