The Sharps lockplate is simple and pretty much the same as most of the back action percussion lockplates of the period. The mainspring is dual action, powering both the tumbler and the sear, again a pretty common arrangement.
The Lawrence primer mechanism won't interfere with replacing the mainspring.
The only tool needed for replacing the spring would be a good spring vise or a machinist's clamp; I recommend a spring vise. Pad the jaws with tape if you want to be sure not to scratch the new spring. If you want to disassemble the lock, you should get a good gunsmith's screwdriver of the proper size. If the lock is rusty or the screws are frozen, it might be better to oil the lockwork and leave it alone rather than taking a chance of really messing things up.
Jim