what if she was just dogging the Winchester's heels to keep them (and the angels) busy while she was breaking seals..maybe she was testing Sam's powers..remember Croatoan, where they were testing to see if Sam was immune to the demon infection..
and i think the attempt at a deal was a check of Sam's mental status..Sam had to choose, of his own free will, to kill Lilith...he had to be so focused on killing her, that nothing, not even a deal to end the breaking of the seals would sway him..
remember also the conversation with Dean when he asked Sam if he had considered taking the deal or not, where Sam made it a point to vehemently deny he ever considered the deal...and Dean's reaction to the statement..

I am not sure just yet. I do think they are trying to turn Sam, and that Croatoan was a test. But I am not sure she was checking his progress level. Sam has changed alot though. I'm hoping things will turn out okay.

I actually think you have a great point Lucy. It might have all been a huge test, but I'm not sure if it was Lilith administering it. I think that the test giver might have been Ruby. Cause you know how she said at the end that she was Lucifer's most faithful servant. But it could also be the both of them in it together. Because she did say that Lilith was the only one who knew, which might be why Ruby got out of hell so easy in the beginning of the fourth season. Because I don't really believe that she'd have gotten out without any help.
But again Lucy, you do have a valid point. :)

Now that we know that Lilith and Ruby were in this together all along, some things from that episode seem to make a lot more sense! Testing Sam's power is very plausible. Looking back, I don't think she ever intended to kill him. The whole purpose was to make him believe that she couldn't, so he would pursue her and never give a second thought as to why she didn't just kill him to get him off her trail. She and Ruby also hatched the scheme to have Lilith take over Ruby's "body" and then pretend to have sent Ruby back to Hell - so when Ruby showed up in Season 4 saying that Lilith had given her another chance, again Sam would have no reason to be suspicious. You make a very good point, Lucy, that Lilith had to find out how committed Sam was to pursuing her to the end. When he didn't take the deal and tried to kill her instead, I guess she had her answer! :))

Hmmm, nahh, t just wouldn't do to have Sam suspicious Lilith wasn't out to get him, and to agree with you lot a bit, maybe she wanted to know if they had the right guy: Sam had died, he'd have ended up in Hell right alongside Dean, and they would have two less hunters to worry about. And the Demons didn't seem to be in an extreme rush, they could have gone around again to get them babies juiced up for another round, cause like Salvation showed, they kept going after other children, just in case someone flaked.

So no, I don't think Lilith was checking how hard Sam could be if he flexed... (Now I am thinking of Sammy flexing... noice!)

uhh good idea never thought of that. Yea. Coz they wanted Sam alive so she couldnt of been trying to kill him. So she must of been doing something else, and checking his power is a good idea.!