If you have been rebooked to other flights and then later LX reinstates the flights and you want to get rebooked, you need to contact UA who issued the ticket and it will be viewed as a voluntary change to be dealt with according to the ticket rules. But to answer your Q: No, once rebooked the UA system will not rebook you automatically if/when better suited flights become available. If you want to rebook again you need to find out yourself and contact UA for rebooking.
LX will not touch a ticket issued by UA.