I wish to apply to another firm, if I am offered a TC by the new firm would I be able to recover my lpc and housing costs to return to my old firm with whom I already hold a TC?

It’s common for hiring firms to pay out lpc or similar costs that you may owe a current employer.

You probably have a clawback clause in your employment contract. The amount you owe likely reduces by a certain percentage at every six month interval of full time employment with your current employer. Whatever amount is owed under this clawback clause is what the new firm would cover, with their own clawback clause of course.

It will be up to you to negotiate this as part of your salary, signing bonus (if any) and general employment terms.