Male lions dont usually hunt unless they're older and thus out of the pack or younger and not yet in a pack. Generally if they're in a pack, they dont hunt.
So you have any one of three lions:
a) the more experienced but aged and more feeble lion
b) the less experienced but younger generally more fit lion
c) the varied level of experience and age lion that is sick or injured and thus lost his pride support.
Looking at the bear, it gets the treatment of being raised by mom, and fighting all its life for its own food after mom says get the hell away from me. So at any age (within reason) it has the experience to use it.
Looking at age, it stands:
bear: generally lives to be 30 years old (average, good conditions).
lion: 15 years (in the wild, where it would get the best "training" for this fight).
So alraedy the bear can live to be twice as old as the lion and still in prime state.
Grizzlies also have a more balanced diet, do I have to give the bear the nod for that.
Then you have size. Now, since we're talking a bout a female grizzly, its somewhat hindered, and its protecting its cubs, so its mind will be divided. but we'll go with it (though itd be better and more fair to say a male on male fight):
bear: can be over 5 ft standing, 3'5 on all fours, 6'6 long, 440 lbs.
Lion: 4 ft tall, 5'9 long, 550 lbs (average)
So while the lion is heavier, the grizzly is taller standing, and with a powerful swipe can just knock the lion aside (with potential to serious injury landing).
and just from some personal experience, i've seen black bear, and at one point hunted one. they are NOT fun to hunt, and it was quite literally life and death when it came down to the last moments. and since grizzly get the nod for being tougher then black bear, I'm going to only assume that the grizzly would have been twice as bad. Just from that, and what i've read and heard about lion attacks, i dont think it would stand up.
So in the end, (I think) the winnner would be:
http://www.firstpeople.us/pictures/bear/odd_sizes/Angry-Grizzly-Bear.jpg
...
but thats all meaningless,
<spoiler=cause everyone knows everything pales in comparison to Teddy>http://3.bp.blogspot.com/-HlzshdUFnpU/TX4sj4-zf2I/AAAAAAAAAIc/Z6bsiP8Y5N8/s1600/teddy_roosevelt_pointing.jpg
hed kill both, bare handed, alone, at the same time, on his death bed.
cause you just dont talk about bears or who's toughest without talking about teddy
EDIT:
<url=http://www.askabiologist.org.uk/answers/viewtopic.php?id=546>and at least one "biologist" seems to agree.