I can only give you my opinion based on these few facts.
The leafs wants are depth at the Center (prospects and NHL ready) and Right Defense (NHL ready)
The Leafs have no trouble scoring or moving the puck. They have good special teams players
They are lacking solid defensive Dmen and have a tough time regaining possession and clearing the puck probably in part by their defensive system and of course their personnel.
-I’m ok with trading Bracco because the Leafs are very deep on the RW. I like him very much but there is just no room at the moment.
-Liljegren was in the race to be drafted in the top 3 in 2017 before he was sidelined with Mononucleosis and missed a huge part of the season leading up to the draft and his stock dropped. I was amazed he was still available when the leafs grabbed him at 17. After watching Liljegren adjust to the NA game this year and now seeing him in the AHL playoffs, I’m not moving this guy. He looks like he is going to be a stud.
-They are already saying 2018 is comparable to the 2003 NHL draft in regards to depth and even though the leafs are drafting in the 20’s there will be some good Centers available. I’d move the 2019 first not the 2018.
-I like Barrie but he is what the leafs already have, a offensive minded puck moving Dman who gets caught out of position at times. Yes he has a right handed shot but I have to believe, and I hope and Pray, that the leafs are looking for more defensive minded shut-down role Dmen who can compliment Reilly, Dermott and Gardiner and help stabilize the back end.
So for those reasons I think the Leafs decline.

I like what @SirCharles said I think he's 100 on the button. I will add 1 thing though.

Considering that the Leafs are giving up the most you'd think the Leafs would be getting the best player.

I don't know if it's as simple a second maybe adding a Tyson Jost to Toronto or rearranging entirely who gets what. It is a great though, I just don't think after the Duchene deal, the Sens aren't going to be quick to deal with Avs again.

Are you saying Liljegren can jump into the Leafs line up next year and be an impactful Defensemen?

I don't see Toronto giving up Lijegren++ to get Barrie.

i wouldn't do lilegren for barrie straight up. leafs don't need another small puck moving d man. they need a d man who is reliable in his own end

Unsure how any of what I said gave you that impression.
No I never said that and I do expect Toronto to make a move, just not this one.

Relax, it was a question. Don't know much about Liljeberg and since you've apparently seen him play, thought you might be able to give some insight?

HaHa I'm very relaxed! Again, I don't see how I gave you the impression of being emotional... Not sure what I can do to convey how I'm feeling, maybe emoji's ? Yea, I seen him a couple times earlier in the season and you could tell he was a bit green but talented and real fast. He seems to play with more poise now and seems not to second guess himself. He stands out. That said I think he needs to get stronger and have a big summer. I actually would expect to see him called up for maybe a game or two next season, if all goes well, but I guess that'll depend on what the Leafs do to address their woes in the off season. Even though the Leafs had a good season the D-group looked like it had holes in 70% of the games... They can't break the cycle down low and are not strong enough to fight off forecheckers to win the possession battles. God only knows why or when it became cool to try to clear the puck through the middle of the ice... maybe because they are too weak to force it out on the boards... In anycase they need a couple of guys that can be a bit tougher.
All my time in hockey we were always taught when defending to use our body on the opposition to separate man from puck... All the leafs beside Reilly, Hainsey and Polak jab at the puck... I suspect even though fans don't like Polak that's way Babcock does. If they jab at the puck and miss they are screwed position wise. Hense, why Gardiner gets beat so often. I'm not saying you need to destroy players with big hits, just get in their way and slow them down, stay between them and the net. The Leafs need more of that. Hjalmarsson, Boumeester, McNabb either one of these guys would make a huge difference. May have an effect like Hainsey does for Reilly, Everything seems much more stable when he is on the ice.

Honestly, I am not the biggest Babcock Fan. I mean, I know he has is awesome CV but he seems extremely stubborn and throughout the season, he'll pick up favourites that he'll go to, night in and night out, regardless of how well they're playing (usually grizzled vets). Can't see him trusting and playing a 1999 Defensemen on the backend for at least another maybe 2 / probably 3 years regardless how good he is in the Jungle.