Depends on how you use the phone.
Battery Life on my Skyrocket is bad on LTE if you're a moderate to heavy user. On the Vivid it's even worse (used to own it). If you're on LTE and you start using the phone at 8 am on LTE by the time you get to noon time you're already going to be turning off stuff like GPS or maybe toggling airplane mode here and there to save battery. Neither of these phones can last a full work day on moderate to heavy use on LTE.
Even on HSPA+ my Skyrocket and the Vivid would die by 3-4pm if I did quite a bit of Facebook Chat, Texting, or Web Surfing on it.
A lot of it has to do with how much power the SCREEN uses, cause I know when I used to tether my iPod Touch 4th Gen to my HD7 with a 1230 mAh battery on HSPA+ it could still last all day tethering the iTouch, but the battery would drain fast if I wasn't tethering and actually used the phone cause the screen kills the battery.
You don't want to give her a Vivid, TBH. Save money and get her an 8GB iPhone 4 or something, or perhaps a $99 4S. Not trying to start a debate, but those phones clearly have better battery life since they don't run as many things in the background and the software is a bit more optimized than the Android 4.0.3 + Sense 3.6 on the Vivid. Another decent choice would be the Atrix 2 (HSPA+ only, no WiFi direct or NFC but otherwise similar specs - 16GB SD Cards are cheap at Best Buy). The XPeria ion is actually a good choice as well, with LTE, SD Card Slot, better battery life, and a much better screen for a cheap price. The price may go down soon as the TL is coming to AT&T in a few days for $99 so if you can afford that you may want to wait. Not sure when the Windows 8 phones are coming, but if she has a Notebook you can upgrade for cheap that would be an optimal choice if she also uses a computer. They tie in very nicely together.
I wouldn't get a Vivid on contract at this point, personally. Not when you can get a One X for $99. It's not worth saving that much (as in, not really a lot of) money.