When I import videos from my Lumix DMC-LX5, the Capture Date is set to the date/time of when the video was imported. Photos do not have this problem. The files are imported as MTS files.
Unfortunately, LR doesn't properly read or write video metadata. Please vote and add your opinion to this topic in the official feedback forum:
as a workaround you can use exiftool to modify the file date and import the files.
exiftool "-FileModifyDate<TrackCreateDate" "-FileCreateDate<TrackCreateDate" *.mts