What is the difference between the following two sentences
I would die before I lied
I would die before I lie
Is the first one in subjunctive mood?
I would die before I lied.
I would die before I lie.
No: subjunctive clauses are headed by a plain form of the verb, e.g. "I insisted [that he meet her]". But "lied" is past tense so it can't be subjunctive.
In any case, only a very few prepositions, like "if", "unless", "lest" etc. license subjunctives, so neither of your examples qualify.