LTSpice is inteded to encorage you to use the chips from Linear Technology, that's why all their range of opamps are available in the library ...
But you can use anything else with little effort. (OK, i've figured that out only a few weeks ago

)
First of all, you can use a generic, ideal opamp out-of-the box, by choosing "opamp" at the end of the list and placing it on the schematic. As the comment says, you have to add a SPICE directive to load the corresponding library. To do that, click on the top-right ".op" icon, type
and place the line on the schematic also.
No need for power supplies, as it's perfect and won't distort nor clip.
For more accurate simulations, you can get other .sub files from the website of the manufacturer of the chip. They might have different filename extension, but all are text files full of SPICE models. You can copy the files in the LTspiceIV/lib/sub/ directory, and use the same kind of .lib directive to load the ones you need. Then right-click on the relevant symbol on your schematic, and type in the "value" field the exact name of the model you want to use, as stated after ".SUBCKT" in the model.
That's it !