It could be the kaplan drive, or the Bill Gates Drive,

or it could be the Gladwrap Clinglight drive or Alcoa Aluminum company's starcatcher sail systems.
Of course, one has to make sure a real company is shown in a good light and there might be permission issues involved.
For some fun, one might have a name for each sail type, as they did in the old sailing ships.

If you're using a solar sail to somehow achieve relativistic speeds (moving fast enough for time dilation to have a noticeable effect) I would suggest something along the lines of:

Light Absorption for Relativistic Motion -- LARM

or if you really want to keep "LAMP" as the acronym, I'd suggest something like "Light Absorption for Momentum Projection" of course "projection" would have to have a somewhat tweaked/new usage with your new fancy near-light speed drive for that to work.

If you really like including "photon" it would make the most sense to replace "light" with it. ie. Photon Absorption for Relativistic Motion -- PARM, or ... Relativistic Travel -- PART.

Just trying to add a helping hand. If this is a near-light travel device with an acronym based on the science behind it, and it's essentially some kind of solar drive, using the energy of light from stars to propel it, I would definitely suggest having "relativistic" in there, and some kind of... "light absorption" or "photon absorption" or maybe "light conversion" ie. converting the energy of a photon into kinetic energy (movement)

At the same time, scientists sure do like playing around with words until the acronym is pretty, funny, and/or memorable.

case in point: the proposed Cherenkov radiation detector upgrade in Japan to replace the current one (called Super Kamiokande) is in all seriousness named GADZOOKS! (Gadolinium Antineutrino Detector Zealously Outperforming Old Kamikande, Super!) =P

(edited for typos)

I read PARM drive and got hungry for eggplant.

Light Absorption Module (or Momentum) Propulsion?

Plus, aren't we talking about some kind of ridiculously large laser here? Solar-sail propulsion is slow enough as it is, even with the sun itself providing locomotion. The sheer mass of the laser required to create any kind of significant photon flow would be several orders of magnitude larger than anything we currently have.

*Whew! Too much science!*

Also, once you reach any significant speed and pass beyond the edges of the solar system, you would basically keep going at that same speed - or even increase speed even more slowly due to residual but faint photon reaching your ship from our own sun - until you begin to approach another star and encounter resistance from the photons being emit by it. There shouldn't be any significant barriers to movement in deep space, and you should be able to retain enough inertia that you don't become hopelessly stranded in the wild expanses between stars.

And, finally.... sailors seem to have managed to steer ships in the sea for a few years now without a huge fan onboard to steer the ship. A simple thruster in the role of a rudder, when used in consort with a change in sail geometry and position, would be enough to effect a change in direction. Once you're in deep space, though, you're kind of stuck with the inertia you've got. trying to change it too much would likely require significant amounts of thrust requiring large onboard fuel reserves, or you might risk losing some of the momentum you currently hanve and could end up extending the length of your journey significantly (and when we're talking interstellar distances, a 1% decrease in speed could add up to a considerably longer transit time).

Everyone still with me? Sorry for the digression - it's your technology, so it does what you say it will.

What you say is true, but, there is something to add.
There is photons coming from all over, from the earliest universe to nearby stars. If the light sale was transparent in the direction the ship was moving, then all the thrust from billions of suns would be thrusting the ship along. One simply would have to change sale orientation to change direction.

Remember, the only reason the sky is black, rather than starlight white, is that the universe is expanding. The light of billions of stars that would light the sky like our sun, are cooled by expansion of the universe, sending the energy to heat, rather than light.
That energy is still there, so one just has to have a way to have more force on the backs of the sails than on the front. The use of diffraction and coatings could cause light from the front to avoid the fabrics of the sails and avoid thrust from the light. while in the back, the diffractions and coatings direct the light to the fabric of the sails and cause the push. The difference in light pressure will add up over time. A pound of thrust will eventually add up to near light speed.

I read that if we kept up the thrust of the Apollo launch vehicles, we would achieve light speed in a year.

Light sails are like balloons. You get it big enough compared to your cargo mass. it will get you moving.

Yes, adjustments to the sail would do the job, and would probably aid in retrothrusting, since you could reverse the "polarity", so to speak, as you neared your destination. I'm looking at putting a dedicated fusion reactor on the ship (if the can put a fusion reactor in a ship to power the sucker, they can build a BIG laser and a high efficiency photon sail, just give them a couple thousand years to sort out the details. I'm intrigued by two way mirror style coatings to catch repelled photons before they ever bounce off the sail).