I once played in a Low Life one-shot (written for Savage Worlds Revised, the version out at the time of printing) but used Savage Worlds Deluxe and there were no issues whatsoever, even when incorporating new rules (e.g. the new chase rules, new Incapacitation rules, the Rapid Attack combat maneuver). There are just a couple of tweaks you have to make because Low Life (and the "Primordial Kitchen Soup" campaign) were written for Savage Worlds Revised:
- Convert all melee weapons as follows:
- Str+1 = Str+d4
- Str+2 = Str+d6
- Str+3 = Str+d8
- Drop the Guts skill from any NPCs, use Spirit instead for fear checks (you shouldn't have to given them compensation for dropping the skill, unless you spot an NPC that has a really high Guts in which case you might give them the Brave Edge)
- Change the effects of the Wuss Hindrance from –1 Guts to –1 to fear-based Spirit checks (matching the way that Yellow works in SWD)
- If any NPCs have the waverunner spell, replace it with environmental protection
- (Optional) Use the versions of Illiterate and One Eye that are presented in the core rules, rather than in Low Life
- (Optional) If you have the Kickstarter draft of the new version of Low Life, use the versions of Edges and Hindrances as described there for any NPCs. I can't foresee any reason that they would mess up the campaign.
All of the other changes to the core rules (e.g. Chase Rules, Incapacitation Rules, slight differences to how powers work) will not interfere with your enjoyment of Low Life or the "Primordial Soup Kitchen" campaign.
Players might want to take new Edges and Powers that were introduced in the core rules after Low Life was published, but I don't believe that there are any that wouldn't make sense in the crazy world of Low Life or would interfere with the campaign, so just let them take whatever is in Savage Worlds Deluxe and Low Life.
I don't have access to the new version draft that is available to Kickstarter backers (I wasn't one of them), but I imagine you can probably use the new versions without any issue. If you spot an NPC that has a Hindrance or Edge that exists in the old version, but not the new, then either just use it how it is written in the old version or drop it and replace it with something that exists in the new version.