There's really no down-side to having the same frame as your backup, but I also think that this is a bigger priority for a player who is pursuing some more serious competition and can't afford to throw too many variables into the mix. One consideration with getting the same racquet is to maybe set it up with a slightly different string job if you prefer a slightly softer or firmer layout on different days. I actually enjoy having a racquet strung a few pounds looser for playing outside during the colder months.
As long as it doesn't create a serious distraction for you, it can also be fun to have something different in the bag. If the weight and balance of your backup isn't big-time different from your LM4, it shouldn't be too much of a chore to handle it and generate consistent contact. An alternative can be fun to have, but if the grip shape is different, the flex generates a different sort of performance, etc., it may be tricky to switch back and forth. Not a huge risk, but a possibility to be aware of when you shop another racquet.