Would the Lorica Segmentata have been a good choice of armor in medieval times? Could it have retained its effectiveness on the battlefield, let's say, around 1000 AD?"

The threats on the battlefield of 1,000 AD weren't really much different to those of 100 AD; spears and arrows for the most part, with slingshot, battleaxes and swords also being fairly common. Lorica Segmentata offered adequate protection against all of those, so in that sense it was as good as ever.

However, Lorica Segmentata always had issues competing with chainmail. Even at the height of it's popularity, many romans seem to have favoured chainmail. It's advantages were that it was well suited to mass-production and might have offered superior protection from blunt trauma (although apparently it did worse than mail against dacian falxes). It's downsides were that it was difficult to maintain, generally fit quite badly, had gaps at the armpits and didn't cover the legs at all.

For the feudal nobles of the early medieval period it would have been distinctly inferior to mail; they didn't mass-produce their armour and often fought on horseback where protection from spears stabbing up into the armpit or sword slashes to their legs was pretty important.