It simply means "I would not do evil so that good could come of it", it's a Catholic/Thomistic principle that Tolkien, any Catholic reader would be well aware of being a principle that a chivalrous knight like Faramir would uphold.
The principle of lying so that good may come of it is concretely framed by St. Thomas Aquinas:
I answer that, An action that is naturally evil in respect of its genus can by no means be good and lawful, since in order for an action to be good it must be right in every respect: because good results from a complete cause, while evil results from any single defect, as Dionysius asserts . Now a lie is evil in respect of its genus, since it is an action bearing on undue matter. For as words are naturally signs of intellectual acts, it is unnatural and undue for anyone to signify by words something that is not in his mind. Hence the Philosopher says that "lying is in itself evil and to be shunned, while truthfulness is good and worthy of praise." Therefore every lie is a sin, as also Augustine declares.
https://www.newadvent.org/summa/3110.htm#article3
Other things you may describe as lies are tactical maneuvers, not intended as lies, but simply to gain the upperhand in a fight which the opposite side could similarly employ. Two people can't trap each other in the same lie, but two people can distract each other with the same move.
Lying, as Dante would have it, is the absolute worst of all the sins - everybody in the bottom two circles of Hell in his Inferno were either liars or traitors. Avoidance of these things doesn't just make one a noble fool, it makes them worthy of the glories they attain.
But there's more to it than "thou shalt not bearing false witness" deception is also just an offense against the commandments against covetousness.
I answer that, The daughters of covetousness are the vices which arise therefrom, especially in respect of the desire of an end. Now since covetousness is excessive love of possessing riches, it exceeds in two things. For in the first place it exceeds in retaining, and in this respect covetousness gives rise to "insensibility to mercy," because, to wit, a man's heart is not softened by mercy to assist the needy with his riches. On the second place it belongs to covetousness to exceed in receiving, and in this respect covetousness may be considered in two ways. First as in the thought [affectu]. On this way it gives rise to "restlessness," by hindering man with excessive anxiety and care, for "a covetous man shall not be satisfied with money" (Ecclesiastes 5:9). Secondly, it may be considered in the execution [effectu]. On this way the covetous man, in acquiring other people's goods, sometimes employs force, which pertains to "violence," sometimes deceit, and then if he has recourse to words, it is "falsehood," if it be mere words, "perjury" if he confirm his statement by oath; if he has recourse to deeds, and the deceit affects things, we have "fraud"; if persons, then we have "treachery," as in the case of Judas, who betrayed Christ through covetousness.
https://www.newadvent.org/summa/3118.htm
Now, St. Thomas also says that there's nothing that keeps vices things from being classified under two different categories. But covetousness is core to the Lord of the Rings, much more than deceit. Every problem that arises in connection with the One Ring or the dragon's gold is in relation to covetousness. Any time Faramir or the nobler knights attack orcs, it is not to enslave them or plunder from them or in any way take advantage of them. It is simply to drive them back from whence they came and free their people from their threat.
Faramir is a free man because he does not covet. He does not need to be bound by even lies he tells to orcs because he is a free man.
“But even now there is hope left. I will not give you counsel, saying do this or do that. for not in doing or contriving, nor in choosing between this course and another, can I avail; but only in knowing what was and is, and in part what shall be. But this I will say to you: your Quest stands upon the edge of a knife. Stray but a little and it will fail, to the ruin of all. Yet hop remains while all the Company is true.”
Galadriel
any straying, such as going off the path in Mirkwood in the Hobbit, is straying a little - which will cause the Quest to fail.