I know a thing or four about Power Play, and Mining Lances - I have quite a few of them actually.
They are a Power Play reward item. You have to be pledged to Zermina Torval for a period of Four Weeks (that's a month), and by the fourth week you must reach at least rank 3. Once these conditions have been met, you may purchase Mining Lances from a wide number of stations. If you quit Power Play, or your rank drops below Rank 3, you will no longer be able to purchase Mining Lances, however you may keep and use any you have purchased.
As a module is concerned, these are Fixed, Class 1 weapons. As a weapon, they are... a bit underwhelming, though I did once fry a sidewinder with mine. They do produce a fair bit of heat, and have a fairly high power draw, but on a dedicated mining ship, like a Type-9, they work quite nicely. With a 2km range, you can have a rock about half stripped by the time you're in range of standard mining lasers and optimal limpet range.
Power Play is as complicated or as easy as you want to make it. I generally do my part by delivering Fortification goods. I'm not interested in PvP, and while not unfamiliar with Combat in general, it's not my main reason for playing. Most of the time I'm perfectly content hauling passengers around or mining.
The Mining Lance can also be quite useful as part of a Mining Pair - that is one Lance, one regular Laser - ideally a Class 2 Laser with the Class 1 Lance, allowing you to get a good head start stripping a rock before you close to Mining Laser Range, and the heat generation and power demands are pretty reasonable and this pairing is quite effective.