Is it possible to detect or localize movement of objects using LPWA (or LPWAN) such as LoRa, DASH7, NB-FI?
Yes, the Doppler effect applies to any electromagnetic wave. No matter whether that is an actual Radar pulse, or a microwave oven falling from an office tower, or a passenger aircraft's transponder, or an LPWAN device.

But, this possibility is especially limited for LPWAN devices, as I'll explain below.

Low Doppler shift due to low carrier frequency

The higher the frequency, the more Doppler, and for some reason you picked particularly low-frequency standards, all operating 1 GHz, making the Doppler shift you get smaller, compared to other uncertainties like local oscillator frequency errors of the typically cheap devices.

Need for Frequency estimation

Short pulses make estimation hard

There's a basic mathematical truth that for a frequency estimate to be fine, you need a long observation, and conversely, for a time estimate to be fine, you need a large bandwidth.

Now, these standards use short transmissions, bursts, because the batteries won't allow them anything else. So that severely limits the time, or energy, you get to estimate frequency. Since you probably don't know in which general direction your LPWAN devices are moving, you'd want an unbiased estimator. Armed with a relatively simple SNR number, you can plug that in to the Cramer-Rao Lower Bound to see how good your frequency estimator of choice will get. And from that it's just multiplication with the speed of light to get the speed estimate variance lower bound. You probably won't like the results.

Cheap devices with no ongoing network registration have bad frequency accuracy

For Doppler estimation to work, you need to be able to estimate the frequency shift of a device. To achieve that, either the device needs to transmit at a very precisely known frequency, by either having a very good oscillator itself, or by "learning" the right frequency from a base station.

Both principles are pretty much impossible for LPWAN devices; they need to be cheap and low-power, so no high-quality oscillator that could run continuously. Also, no "waking up, synching to a base station, correcting the frequency offset one has by complicated algorithms, sending three bytes, going back to sleep", so also the second option is out.

Location estimates hampered by low bandwidth

So, in absence of good transmit frequency knowledge, you could simply observe the same transmitter from multiple points and estimate the speed of movement and the direction through getting enough equations to compensate for the unknowns, right?

Yes. In essence, you'd be building the "inverse" of GPS. Problem: GPS is especially designed to make getting the pseudorange and frequency estimates possible. It sends a relatively wideband, pseudo-white sequence, to make it easy to estimate a sharp crosscorrelation peak.

Your systems are designed to be narrowband and pretty much invariant to static frequency shifts, and hence (see point "short pulses..." above) do not allow for accurate time or frequency recovery.

You basically always run into the fact that these are the worst signals for frequency and/or location detection.

General remarks

I've never heard of DASH7 and NB-FI, but realize the first is just an abused RFID standard, and the second exists as invention of a single company, like there's dozens of companies who just wanted to grab some cash on the IoT goldrush, so honestly, probably not the relevant standards in the future.