I was going through all the changes they made to the skills and saw that you can now chain different skills together. My favorite chain would be Shield Barrage - Spring Attack - Wallop - Super Leap which works perfectly when you can safely attack the boss. Also it's great that Super Leap also blocks frontal damage like Wallop. Onslaught is pretty good in that regard now that it blocks too. Also they seem to have fixed the Onslaught desyncing.
As for the new skills, I always chain Super Leap after Wallop or Charging Lunge when Wallop is on cd to avoid the awkward jumping behind the boss and messing up my position. I'd say the other "chains" (as much as you can call them so because you can't really have a set rotation on a lancer) are fairly similar to how they used to be. I'll give you a list of how all the skills can be chained now (to my knowledge):
Charging Lunge -> Super Leap
Wallop -> Super Leap
* I prefer chaining Super Leap after Wallop but I chain it after Charging Lunge when Wallop is on cd. I like chaining it after Charging Lunge when crossing a distance to the boss though or after push attacks to quickly return to the safe field around the boss (like in Thaumetal Refinery 1st boss). It's great that it blocks frontal damage. Make sure to always chain it to avoid jumping behind the boss.
* I use this when Shield Barrage is on cd to get or to keep my Debilitate stacks. So it's simply Debilitate -> Shield Bash -> Onslaught (for skill attack speed). I am really happy to finally be using Onslaught after the desync fix, before that it was just an unusable skill in my bar!
* I have not tested this out myself, it's supposed to give you a faster Shield Barrage. I read an advice saying you should use the first hit of the Combo Attack by block cancelling it instead of using the 3 full hits of the Combo Attack.
I only use Combo Attack when everything is on cd or I need a bit of mana so I'm not used to this but I tried it to see and the Shield Barrage does get a little faster.
* So I think using Challenging Shout before Chained Leash should pull the far away targets to you. I like using this in Thaumetal Refinery and Lilith's Keep with hallway mobs: Challenging Shout -> Chained Leash -> Charging Lunge -< Super Leap to knock them up in the air! Then I continue with my usual attack chains.
The new skill Divine Protection is useful in Thaumetal Refinery 1st boss when you screw up the banana and the field goes red. Same thing for the 3rd boss when the goblin walks through the puddle and the field goes red, you just have to use it very quickly before you get stunned. I haven't tried it myself on the lasers on the 2nd boss but I read that it works so I can imagine it being useful if lasers appear when the boss is nearly dead and you just want to keep dpsing.
Also useful for the bird lunging down in Ravenous Gorge. I imagine it would protect you or your party memebers from getting one shot when the 2nd boss walks over you when you/them don't hide behind the rock on time.
The big new shield also works for the bird lunging. It works for Lilith's attacks, I try to save it for more damaging attacks of hers as it refects the damage to the attacker. I tried it with the laser on the 2nd boss in Thaumetal Refinery, I had Kaia's Shield on and it still got 2/3 of my hp down. So not sure it works at all there.
Both skills work for the rotating fire of one of the Guardian mission bosses (the one in Balder's).
You can't really guess what are these special boss attacks that those two skills can protect you from, I think we'll all just have to test them ourselves.
PERFECT DEFENSE WITH REGULAR BLOCK
Also, try to make use of "Perfect Defense Success", when you get "Perfect", it's said to refect the damage. I think the on-screen message is "Retribution Shield affects your abilities" or something along those lines.
I am sorry if the advice given is very basic, I am not some pro player so I really just tried to help. If there is some wrong information here, I would happily be corrected and learn something new from more experienced lancers out there!