The Lurk's special ability reads:
Infiltrator
You are not affected by quality or Tier when you bypass security measures.
Does this mean that the Lurk's Fine Lockpicks item also has no effect for a character with this special ability?
Fine lockpicks: A finely crafted set of tools to disable and circumvent locks. [0 load]
Fine items count as +1 bonus in quality, stacking with Tier.
This is an intriguing and complicated issue, best addressed with a group discussion. There are no clear rules to adjudicate this, as far as I know. But, the simple, literal interpretation of Infiltrator's
You are not affected by quality or Tier
is problematic for two reasons:
To avoid these problems, it may be appropriate to reinterpret the literal wording. Reasonably, "You are not affected by quality or Tier..." refers to the PC, without respect to extraordinary factors like items. But, adjudication is up to the players.
A literal interpretation of, "...not affected by quality or Tier...", implies that the PC actually gets progressively worse with acquired experience and resources, rather than progressively better. Or, more plainly, a Tier IV PC without Infiltrator that would otherwise have a relatively easy time with Tier I locks would lose all advantage gained from their Tier by taking Infiltrator. This is a major loss that almost no one would choose willingly, which means its probably too under-powered.
The explication of this ability further clarifies that the PC should not be hindered by opposing quality/tier insofar as it specifies that they "never [reduce]" effect level. 
Fine lockpics are one of the Lurk's special items. Infiltrator is out of the Lurk's playbook, and on a "naive" reading appears to nullify Fine lockpicks. But, it would not nullify any other playbook's special items. Not only is this totally unbalanced, but it creates an especially absurd irony. The whole gist of the Lurk is infiltration and burglary, but on the naive interpretation, it's actually better to take Infiltrator for a PC from literally any other playbook than the Lurk, because it comes at no tradeoff to their special, Fine items. Furthermore, Infiltrator provides no material tradeoff for the cost of nullifying Fine lockpics. There is no opportunity cost to bringing Fine lockpicks on every score, because they are 0 load; they are purely beneficial to the Lurk, at no mechanical cost. So, to nullify them would be a major sacrifice that only yields rewards in exceedingly contrived scenario--e.g. where the PC tries to take on a lock WAY above their abilities. This is far too situational/ niche to warrant the cost of sacrificing the playbook's special item.
If you want to dive into the details a bit in order to make a case to your fellow players, consider the following: Firstly, Infiltrator should only negate any disadvantages (viz. #1) to the PC from being "outclassed" in quality or tier. Secondly, there is a general, here tacit, understanding that the infiltrating PC will make an action roll, and that the action roll follows a procedure. Long story short, at some point in that procedure, the GM announces position and effect, using a set of criteria to evaluate "effect factors". One of these effect factors is Quality/Tier. 
Here we see an example situation, moreover one with Fine lockpics! Notably, this example demonstrates the expected result, but neglects to demonstrate the procedure to get there. Properly, a player can suggest that they want to make an action roll for their PC, before choosing any modifying factors like Fine items. After the GM announces the position/effect level, the player can elect to use a Fine item to their advantage, thereby improving position or effect. In other words, position and effect are much more dynamic and contingent on circumstances than the above example suggests. C.f. TRADING POSITION FOR EFFECT
TRADING POSITION FOR EFFECT
After factors are considered and the GM has announced the effect level, a player might want to trade position for effect, or vice versa. ...
This kind of trade-off isn’t included in the effect factors because it’s not an element the GM should assess when setting the effect level. ...
(emphasis mine)
The "effect factors" Potency, Quality/Tier, and Scale determine the position and effect level. Reasonably, Infiltrator's
not affected by quality or Tier
might be construed to refer to these same initial "effect factors"--namely, those established before any modifications are added or trades are made for position. On this interpretation, the GM would still announce the position/effect as e.g. "Risky/Standard", despite ignoring quality/tier, because scale and potency will still affect position and effect level. At this point, a player ought to be able improve their PC's position with Fine lockpics.
So, as intended, the phrasing of the ability should probably be "You are not hindered by quality or Tier when you bypass security measures."
Or maybe a better way of phrasing the ability is "you are not affected by quality and Tier when bypassing security measures if you don't want to be." The clarification text makes it pretty clear what's going on here:
This ability lets you contend with higher-Tier enemies on equal footing. When you're cracking a safe, picking a lock, or sneaking past elite guards, your effect level is never reduced due to superior Tier or quality level of your opposition.
-- Blades in the Dark, "Playbook: Lurk", p. 74, emphasis mine
If it was supposed to be a double-edged sword, such that your own superior Tier or set of fine lockpicks wouldn't increase your effect level either, the text would say so.
So, a Lurk with this ability and an applicable set of fine lockpicks is always operating at least one effect level higher due to quality and tier effects, regardless of whose lock they're picking or how fine it is.
Do note that this ability does not apply to potency or scale. If there are a hundred bluecoats on patrol (a scale concern) or they've deployed Charterhall's latest Mark VII "Shadow Annihilator" Visibility Beacon (a potency concern), your infiltration effect level is still going to take a hit.
