I agree that it can go beyond a more traditional long history. This year everyone will be talking about Uconn and LSU quite a bit, and certainly those teams, players, and coaches will get a ton of media attention. That makes them big rivals this year even if a long history has not been established.There's some established rivals like ND, Scar, Stanford & Tenn.
Then there's the rivalries based on the popularity of other teams that have some star players that receive extra media attention & hype.
LSU fits into that category & there's even a history where UConn once lost to LSU in an Elite 8 match up in 2007.
In 2008 UConn beat them by 5 in a game played at LSU resulting in a 4-1 all time record betweeen the schools.
No. 1/1 Womens Basketball Earns 74-69 win at No. 6/6 LSU - University of Connecticut Athletics
BATON ROUGE, La. (Feb. 25, 2008) – Freshman Maya Moore (Lawrenceville, Ga.) scored 29 points as the top-ranked University of Connecticut women's basketballuconnhuskies.com
So with Kim as the coach I think LSU can be expected to be rivalry that grows for a number of years to join South Carolina, Notre Dame, Tennessee etc.. I think Stanford almost fit that definition but with their conference status I wouldn't be surprised if their program slipped quite a bit.