They may be compatible, but that compatibility is unnecessary since LP is irrelevant.
For autocraft and inventory management, I have AE2. For everything else, TD does a better job. For that matter, EnderIO does all of that as well with the conduits, AND has inventory management built-in.
LP was amazing back in 1.2.5, it made BC pipes actually function. These days, however, we have better alternatives.
Objectively, no mod can ever be called irrelevant. As long as someone is using it and enjoying it, it very much is relevant for them.
Subjectively, yea, you might think LP is irrelevant, but that's you, not OP, not
@Azzanine, nor anyone else who decides they want to use LP.
As for LP vs other mods. AE2 isn't in every single pack, and while yes, it is in Infinity Evolved, OP has not clarified whether or not they're playing expert mode, in which a LP system is significantly cheaper to get than AE, and is actually capable of doing everything AE can do and then some, with the advantage of not cramming all your items into a lifeless 2 blocks. Alternatively, if OP isn't playing expert mode, who's to say they haven't played with AE2 before, and perhaps this time decided they'd rather try something else. Just because AE is cheaper to set up and expand in terms of resources, doesn't mean you are forced to use it every single world you play (unless you have utterly horrible self control, in which case that's your problem, not anyone else's). As for TD? that does nothing close to what LP provides as a system. And EnderIO? IMO the whole damn premise of that mod is do all the common aspects of modded minecraft better than other mods and for cheaper. It just feels like its designed with the goal of being popular (again opinion, and I realise its an unpopular one at that. EIO isn't the main topic here though).
TL;DR: Please don't try force your opinion on others as though its a fact. Telling someone they're doing it wrong because they're not playing the same way you do.
At any rate, OP already has their answers in the first reply and I've said my piece here now, so I probably won't post in this thread again since I can see this going up in flames very quickly. If you wish to discuss this further Shneeky, I suggest we move it to PM.