Woke up this morning to find that all the lines were frosted and the house was getting warm. It appears that the inside fan works fine (comes on when it gets warmer, runs when thermostat turned to the on position), but the outside unit is running continuously. Guessing that frosting is the result of continuous running of the outside unit without the airflow inside. What is the best guess for the issue? Replace thermostat? Some repair needed to controller for outside unit?

Are you trying to heat or cool the house? its hard to read. The outside unit shouldn`t runn all the time
Several reasons its doing this
Could be a shorted tstat wire,could be a stuck contacter
But you are right, the iceing or freezing up probably caused by the running all the time