Please try to remember that the USN have other assets available to fill those roles that LCS can't fulfill.
What's to remember?
The US had a very good Frigate design, but wanted something smaller, more agile, and that drew less water to act as a COMBAT vessel in the littorals. To go into those waters and take care of three different types of business (three different roles IT was ttasked for) without having to risk one of the other assets you speak of (like a Burke) in doing so.
So, if you want ASW work done, you outfit it with an ASW pack, which I believe will workout just fine. If you want anti-mine work done, you outfit it with its mine warfare pack and I believe that will work fine too.
But in the surface warefare role, the vessel is sorely lacking. Even with the original plan for the NLOS missiles, their range was less than what other corvettes operating in those waters would have...and now, since that program was dropped, they are placing the rediculous Griffin missile package on, which has a range of less than ten miles, and indicating it will be good for "swarming" small craft...like Iranian speed boats.
Oh really? I say they can use the 57mm rapid fire main gun and the two Bushmaster 25mm or 30mm, syncronized automated cannons for that, and the CIWS...but what happens when you face two or three 1,200 ton corvettes, each carrying four missiles that range in excess of fifty miles? I'll tell you what happens...deep kaka!
These vessels (the LCS) should, as a part of their standard package, carry at least one quad cannister (if not two) of the latest Harpoon missiles...at least until a new missile is available that can be launched from an MK-41 (which both variants are capable of installing) or special PVLS implacements.
Otherwise they are going to be going to some potentially wild parties and they will not have the entrance fee required to attend.
If you have to send a Burke with them to defend them everytime you face such a threat...then you have defeated a major reason for building them. And the solution I am speaking of is realtively straight forward. The Harpoon cannisters bolt to the deck and do not penetrate the main deck. They simply need to be wired into fire control and their sensors...and they may require upgrades to the fire control and sensors. But those are cheap compared to facing off against much smaller, and yet much better armed adversaries.