I published a Lola Hayes deck that got some popularity, and someone requested I make a level 0 version, so I tested this deck in solo Night of the Zealot.

"Set-and-forget Lola"

So, the basic premise of this deck is you want to deploy your assets in the first few turns, and then use events to actually take your efficient actions. I'll explain the assets I've chosen and why:

• Magnifying Glass and Boxing Gloves give you their bonuses when you're Investigating or Fighting, respectively. Unlike many assets, you don't actually need to activate their ability to receive their stat bonus. (Compare to Fingerprint Kit or .45 Automatic, for example.) In my opinion, this makes these cards "safer" choices for Lola even if they don't directly enable more efficient uses of your actions. They don't get you extra clues or damage on their own, but another upside is they also don't have limited uses.
• Tooth of Eztli is probably a weird choice to a lot of people, and I'm not in love with it. I chose it for a few reasons: It gives you defensive stats when they matter most (avoiding treachery cards), and brings you to a reasonable 4, It helps you have 7 Seeker cards in your deck, and it's NOT a Mystic or Survivor asset. In my opinion--for this kind of playstyle--It's Lola's best level 0 option.
• Bandolier sucks. Especially the level 0 one. By all means, you could replace it with a better card. It's here because it allows you to have your Boxing Gloves and a Magnifying Glass, but the 2xp Bandolier is much, much better. Because we don't have 7+ Guardian assets, it would make complete sense for you to replace this with Guts or any other card you think is more valuable. Then again, using Boxing Gloves and a Magnifying Glass at the same time is hilarious. Consider that before cutting it.
• Leo De Luca I don't think anyone could consider this a bad choice, but I would understand arguments for other options. In my opinion, not being able to activate any "off class" allies without risk makes them inferior to the extra action every turn. There will be times when you want to draw more cards to help you fight or get clues, and being able to spend actions on draws is sometimes the most efficient thing you can do in this deck. Especially at level 0.
• Shrewd Analysis my understanding (and ArkhamDB's, apparently) is that permanent cards contribute to Lola's deckbuilding restrictions of needing 7 cards from three different classes. The card literally does nothing besides make our life easier, we don't plan on spending experience on vulnerable assets we'll never activate. If you're hardcore or just disagree about my interpretation of the rules, feel free to add a yellow card to your main deck. I'd recommend Shortcut or maybe something like Deduction.

Events

So, as I mentioned before, the main goal of this deck is to use events for efficient actions. Spectral Razor is a quality punch. Read the Signs and Drawn to the Flame grab two clues at a time. Survivor is a little less exciting with Winging It and Improvised Weapon, but Lucky! and Live and Learn make your tests safe, especially with reduced difficulty. Pretty much, it's the best we could do at level 0. If you're not behind on tempo, it can be worth spending actions to overload your hand in order to pitch Improvised Weapon or Winging It so that they fire off for the extra damage or clues.

I'm not sure Emergency Cache is necessary, I didn't need to play it in The Gathering, but I also didn't draw Leo until my last turn. Guts might make your life easier for when you can't blank a Frozen in Fear or something.

Misc.

Besides all that, Plan of Action seemed like the best "extra" yellow card after a minimal amount of consideration on my part. It's either a gravy card draw--There's a player window where you can switch roles after initiating a skill test, before committing cards--or you can go into the Mythos Phase hoping to draw a card with Tooth of Eztli and using this as an Unexpected Courage against brains and feet. It's just a defensive inclusion. Shortcut or Deduction would be more proactive/tempo-positive.

Experience

In my opinion, Studious is the best card Lola can purchase with experience. If you've never used the card, it's insane that you get to start the game (and mulligan from) 7 cards instead of 5. Especially when your goal is to "set-and-forget" in the first few turns like we are, making sure you have the cards you want to put down in your opening hand is so valuable. You look at 7 cards, and can see up to 7 new cards (or more, if you pass over weaknesses)... it's just super good, I think.

Another priority is Boxing Gloves. The resource cost goes down and the goes up, there's not much else to say. If you don't think I'm crazy, Bandolier gives you an extra hand slot which technically allows you to "double" your investigation bonus. I don't know if Bandolier is a more valuable upgrade over other options, though.

Magnifying Glass doesn't change much for us, and I reckon it's not really worth XP. But it is an option and does technically lower the impact on our economy. (And it can help you discard Winging It/Improvised Weapon???)

If your campaign is long enough, I'd seriously consider Charon's Obol after the first scenario. If you happen to be rolling in XP, Another Day, Another Dollar makes beginning the game easier, but there are lots of incremental upgrades you can make to the deck. Adaptable also makes it easy to swap out your Plan of Action if you're not adding new cards to the deck right away, but you've already got Studious. If you want to pick up Charisma, I think Grete Wagner is a decent second ally because she boosts our relevant stats and can soak a fair amount.

Consider migrating your Survivor Suite to Brute Force, Sharp Vision, Resourceful, and True Survivor. I think these cards are all generally better than the level 0 suite, but there are actually merits in both directions. I haven't played the deck enough to know if it's necessary, but Nothing Left to Lose can replenish your hand and resources.

The experience versions of A Test of Will (A Test of Will) are much, much better for Lola because you cancel the card no matter what. The level 0 version relies on you passing 3 against 3 which just isn't very likely.