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This answer reminded me that the Electron rocket drops one of it's batteries when it is mostly spent. We might call that "micro-staging".

This answer quotes Spaceflight 101:

With a low auto-ignition temperature of only 150°C, the second stage batteries will burn up in their entirety during re-entry while the first stage batteries are also likely to be incinerated to some extent during their sub-orbital re-entry.

The phrase "...likely to be incinerated to some extent..." is a bit vague and half-hearted.

Is there any further information on this? Do they hit the water in burning lithium and plastic flames, or do they dissipate before impact?

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    $\begingroup$ New Zealand changed or at least assessed it's law to allow for rocketlab launches: Regulatory Impact Statement: Regulation of deposit of jettisoned material from space vehicle launches under the Exclusive Economic Zone and Continental Shelf (Environmental Effects) Act2012. It also mentions batteries impact on the ocean. Citation: "Information from Rocket Lab notes that lithium batteries are expected to burn up completely during descent rather than be deposited.". $\endgroup$
    – Christoph
    Commented Apr 17, 2019 at 6:40
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    $\begingroup$ @Christoph thanks for that! "...expected to burn up completely..." is definitely different than "...likely to be incinerated to some extent..." Hmm... I wonder if they are telling different stories to different people!? $\endgroup$
    – uhoh
    Commented Apr 17, 2019 at 15:03
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    $\begingroup$ @uhoh It seems impossible that the first-stage batteries burn up during their descent. By definition, they're jettinosed well before MECO. In this launch: youtube.com/watch?v=SNuauG1Gvr8, at MECO the Electron rocket was at an altitude of 77.8 km; jettisoning must have happened well before that. This article spaceflight101.com/spacerockets/electron states that the used batteries have an auto-ignition temperature of 150° C; it seems not sure at all that this temperature is reached, by atmospheric friction, during a fall from some tens of kilometers. $\endgroup$
    – Jan van Oort
    Commented Aug 24, 2019 at 12:30
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    $\begingroup$ @JanvanOort thanks, but I think you are mostly just reiterating the content of the question. $\endgroup$
    – uhoh
    Commented Aug 24, 2019 at 12:48
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    $\begingroup$ @JanvanOort okay, 150C is already in the question, and "well below 77.8 km" isn't a number yet. ;-) I think the altitude of the battery hot-swap event can be obtained from some of the Rocketlabs launch videos, they sometimes announce the event, and I think I've actually seen one drop in one of the videos. $\endgroup$
    – uhoh
    Commented Aug 24, 2019 at 12:59

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The question turns out to be a bit misguided as the first stage batteries are not ejected during flight; however, it can still be answered no.

Spaceflight 101's quality can be mediocre at times. I think this article is an example of that.

I found no evidence that states that the first stage batteries are dumped overboard during flight. The Electron Payload User's Guide explicitly states this for the second stage (emphasis added):

High Voltage Batteries (HVBs) batteries provide power to the LOx and kerosene pumps [...] During the second stage burn, two HVBs power the electric pumps until depletion, when a third HVB takes over for the remainder of the second stage burn. Upon depletion, the first two HVBs are jettisoned from Electron to reduce mass and increase performance in flight.

There is no such statement for the first stage. Additionally, looking at the layout of the vehicle in various pictures I see no clear mechanism for ejecting the first stage batteries short of also jettisoning all 9 engines. From the User's Guide the batteries (power pack) are located between the tanks and engines, probably around the engine plumbing: first stage power pack

Close up pictures don't seem to show anything either from the bottom or side: close up 1

Credit: Rocket Lab, from Spaceflight 101

close up 2

Credit: Rocket Lab, from Spaceflight Now article

close up 3

Credit: Rocket Lab, from Engadget article

The incineration part is basically DOA because we know that Rocket Lab is pursuing recovery and eventual re-use of the Electron booster. They have already fished-out a flown booster and because the batteries remain onboard they are not exposed to the heat of re-entry.

The main concern for Rocket Lab is the heating on the engines and they make no mention of protecting the power pack. I suspect that there is very little heat transferred to the batteries during the brief, but fiery re-entry period. Additionally, the toxic flames of burning batteries could damage electrical connectors (among countless other things) and would also be a risk to humans involved in any recovery operations (and protective instruments are not seen in limited pictures).

This screenshot from Everyday Astronaut's Rocket Lab tour video appears to confirm the radial battery placement and definitely shows just how impregnated they are inside the vehicle:

technician working on power pack

It also shows the individual "battery units" covered in (presumably) some kind of multi-layer insulation. Batteries have some of the strictest temperature limits of all space hardware (slide 5)*. Such tight limits necessitates ample engineering effort towards their thermal control.

*this table is likely referring to older nickel based space batteries, but lithium based batteries still have tight limits.

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