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I would just tow it to a Lexus dealer and let them fix the mess.
They more than likely have encountered this before and can tie 12v into the backup light socket, or the door mirrors and get the relay to unlock the door.
You could ask several Locksmiths if they have a "break-in specialist" on their staff, or a freelance one they hire when needed for a particular job. These guys have special tools and skills and can open most locked vehicles in 30 seconds. The disadvantage of this option is there is typically some residual damage to a weatherstrip or interior trim piece, and it might cost ~$100 to have them replaced.
A sort of "last resort" option would be to break the small window just forward of the outside mirror, then reach in and manually unlock that door. You might inquire at some body shops the cost to replace that window. My guess is ~$300, as the side window and its guide must be first removed to access the small window. I estimate someone who has done it before should be able to to accomplish the task in less than 2 hours.
You stated that the "mechanical" key is not truly "mechanical", so can you please explain how you can "manually unlock" the door?
To (attempt to) answer your "Locksmith" question, I performed some experiments on my NX. The short answer appears to be NO; a locksmith cannot help you.
Why not? . . . it turns out the "mechanical key" is not mechanical in the traditional sense, it that it does not mechanically unlock the door. Instead, rotating it clockwise operates an electrical switch that powers the door actuator(s). So the mechanical key is useless with a dead battery. I proved this theory with the following experiment:
(1) With hood and drivers window open, I reached in and locked the doors. The "mechanical" key worked as described above to unlock them.
(2) Next I removed the "Door Lock #1" fuse (20A; located in the under-hood relay/fuse box). Rotating the "mechanical" key now had no effect whatsoever. In my view, this is a silly and ineffective design by Toyota/Lexus, and not clearly disclosed in the Owners Manual.
Reviewing the wiring diagrams, I noticed Lexus includes an optional door lock backup battery in some markets, mounted in the center console. This allows the door locks to still operate even with a dead or disconnected main battery. Unfortunately, this useful feature is not included in NX300 models offered for sale in the USA (or probably Canada). I do not know if the hybrid model includes it.
After raising each front tire with the jack, I recommend to lower it back onto something solid like one or more concrete paving blocks or scrap boards. This is more secure than the jack itself, and will not obstruct the space you need to work within. Jack stands, if you have a pair, could be used as well.
I think you are right, lexus mechanical key is a "genius design", without the battery or the battery is completely dead, you won't be able to open the door with the mechanical key, that's true. I'm still waiting the car jack arrive, much tks
the "mechanical key" is not mechanical in the traditional sense, it that it does not mechanically unlock the door. Instead, rotating it clockwise operates an electrical switch that powers the door actuator(s). So the mechanical key is useless with a dead battery. I proved this theory with the following experiment:
(1) With hood and drivers window open, I reached in and locked the doors. The "mechanical" key worked as described above to unlock them.
(2) Next I removed the "Door Lock #1" fuse (20A; located in the under-hood relay/fuse box). Rotating the "mechanical" key now had no effect whatsoever. In my view, this is a silly and ineffective design by Toyota/Lexus, and not clearly disclosed in the Owners Manual.
That's an interesting finding. Fortunately, the mechanical key for mine works on a dead battery, verified several times over now.
Now that I realize I cannot depend on the "mechanical key" to open the vehicle in case someone accidentally leaves the headlights on, or the main battery dies for some other reason with the doors locked, I decided to install a hidden backup hood release. Lexus conveniently provided a second set of cable mount fittings on the hood latch, I assume to accommodate right-hand-drive models. I already had a spare bicycle brake cable that had been gathering dust for probably 25 years, so this was a no-cost project that only required 30 minutes of time. The operating end is hidden from view by the casual observer, and works perfectly.
Details in attached images.
Image 1: Hood latch. Extra fittings for a right side release cable are circled (assumed to be a provision for right-hand-drive models).
Image 2: Bicycle brake cable installed. Yellow material is a liberal application of lithium grease.
Image 3: Cable routing along the front apron.
Image 4: Cable routing along the right fender. From there, it passes under the washer fluid filler mounting bracket, and then down toward the right fog light. A piece of plastic wiring harness loom was added to protect the cable.
Image 5: Remove these 4 10mm screws to lower the front right valence section. Reach in and position the cable in the desired location.
Image 6: I chose to have the cable exit at the edge of the lower engine cover. It tucks up on top of the cover and is not visible to the casual observer.
Image 7: A short piece of shrink tubing, heated only at the tip, serves as a protective weather sheath. The exposed end of the cable is liberally greased as well, with waterproof grease. The sheath slides off easily in order to operate the emergency hood release.