I am attempting to identify any organic compounds that exist in an H2SO4 sample which contains percent level of metals. Any suggestions? Would LCMS work? If so what conditions (column, interface, etc.) would be necessary?

LC/MS will give a molecular weight, but you might not get much structural info without MS/MS. If you only have a single quad, you can run the sample with successively higher fragmentor voltage / declustering potential / whatever to get fragments (poor man's MS/MS).

If these are complete unknowns, I suggest a C18 column with a long slow gradient, A = water + 0.1% modifier, B = acetonitrile + 0.1% modifier. Modifier could be acetic or formic acid (for pH control and for your electrospray signal). Try running in both negative and positive mode electrospray, and APCI too if you're ambitious. Some neutral organics might not ionize and you won't see them.

If this is concentrated acid, I suggest either diluting it until it is in the millimolar range, or neutralizing it with ammonium hydroxide. Neither your column nor the stainless steel parts of your ion source held at ~350°C will like being hit with conc H2SO4. If you have a divert valve, I suggest diverting your column eluent to waste until after the void volume has eluted. Otherwise sulfate salts etc. will build up in the ion source with each injection.