Right to clarify a few points,
There are several factions you can make armies from to take a warband from a faction you take one hero from that faction and can then take 12 warriors from the same faction.
In this case there are two factions, Rivendel and Lothlorien + Mirkwood (Lothlorien and Mirkwood count as the same list, I guess because its easy as they both include wood elves. If you want to only take lothlorien just use lothlorien heroes).
So can lothlorien and rivendel be in the same army? Absolutely!
Just take one rivendel hero, say Elrond, and one lothlorien hero say galdariel, then pick up to 12 warriors each for their warbands. Simple
Don't be put off about using them, if this is an army you like the idea, theme, look of then you won't be disappointed. Armoured elves don't normally have numbers on their side so they can take some practice to use effectively on the field but they are a good army once you've got the hang of it.
Quick note, there are a few odd bits from the new hobbit lists and the old sourcebook lists as jamesR has pointed out.
A rivendel list has armoured high elves on foot, to ally in Rivendel Knights you have to ally in the Elrond;s Household list.
To take Mirkwood elves from the sourcebook you could take say Thranduril and then upgrade archers in his warband to hit on 2+. You'd then have to use the new hobbit sourcebook list to ally in mirkwood rangers.
Can seem very confusing especially when people like Elrond, Legolas and Thranduril appear in more than one faction (you can only ever take one of a named character btw so no multiple legolas's
).It's quite simple once you get your head round it
Hope that helps