First it doesn’t need additional filtering and i’m pretty sure the filter would block the DC required to supply the LNA with power.
Second calling the Raspberry Pi a piaware is all kinds of confusing, it sounded to me like you would replace the dongle at a later point in time.
No matter, you can indeed power the LNA with the Airspy via the coax.
But the airspy needs some configuration to work with piaware, it’s not really a problem though:
HOWTO: Airspy mini and Airspy R2: Piaware / dump1090-fa configuration
With the bias-t powering this particular LNA, the airspy draws quite a bit of USB current, which can be a bottleneck.
Thus i prefer powering this LNA with an external bias-t.
Also means i can reduce the feed voltage to 3.5 V with a 20 Ohm resistor using the 5 V from the Pi. That way the LNA runs a good bit cooler.
If you have a rather long cable run between bias-t and antenna i’d probably only use 10 Ohms or so.