To sort of echo what Chrome said, really you can defeat any monster using a lance. Just like any monster in any MH game, its just about recognizing their attack pattern and being able to defend yourself; the lance is a great weapon because blocking doesn't cut into health, you're mobile while blocking, and it doesn't affect sharpness like if you were using a GS. Just don't get blasted by a thunder attack; i'm not sure you can block it. I know you can't block an Agnaktor's fire-beam, so I'd have to check it out.
Switch Axe is what I used to defeat him. Not sure the exact name of the weapon but I know it was 100% upgraded. I'd also work hard to get water armor so he doesn't deal massive damage to you.
Thanks, rychus! I'll try to work on my ability with the Switch Axe, I wanted to be good with it at first, but took me a long time to do any good with it.
The Lagiacrus is weak to fire, however the only fire lance available is the Agnaktor Spiral Heat/Agnaktor Firelance line. There are more early options available for S&S, however, and that may be desirable considering the Lagia's decent speed. You would have two choices here; The Qurepeco Bone Tomahawk, which is powerful but also singular (in its line) and has very poor sharpness, or the Qurupeco Chopper, which is less powerful, but evolves later into the Blazing Falchion of the Rathalos line.
One more thing to consider is that the majority of the fight will take place under water, so regardless of what weapon you choose, it's important for you to be good enough with it to stay mobile, because I remember Lagiacrus loving his ramming attacks.
As for elements, fire works the best as mentioned before. Defense-wise, I'd favor electricity over water defense, since that helps you against both his projectile attack and his more dangerous attacks in general.
