No, you cannot use ad in this way, because ad is a preposition with the accusative. Even if you could, it would still not help you, because ad simply doesn't mean “until.”
For “until,” the usual Latin equivalents are dum, donec and quoad. They all have the somewhat irritating property that they can also mean “so long as” or “while.” The famous Dum spiro, spero obviously does not mean “I hope until I breathe” – but you have to interpret that from context.
In the “while” meaning, the indicative is used. (Or at least that is what is taught as good classical prose composition – the real picture is somewhat more complicated.)
But in the “until” meaning, both the indicative and the subjunctive are found. If you peruse Latin grammar books, you'll find a certain variety of attempts to systematize, explain and express the reasons for using either one; but in general, the gist is that the subjunctive expresses some desired outcome that the subject of the main clause wants to bring about or await. It is frequently used with verbs of waiting, remaining, holding back, etc. to give something else time to happen. The indicative, on the other hand, is used when the speaker does not want to express such an intent, either because it does not exist or he does not want to emphasize it.
A good example for the indicative would be (Sueton, Divus Iulius 82):
[Caesar] exanimis […] aliquamdiu iacuit, donec […] tres servoli domum rettulerunt.
Caesar lay dead for a while, until he was carried back home by three slaves.
A good example for the subjunctive would be (Cicero, Tusc. 4, 36):
His [iratis] subtrahendi sunt ei, in quos impetum conantur facere, dum se ipsi colligant.
Angry people must be denied access to those they try to attack until they have collected themselves.
(Note: Cicero and Caesar never used donec in the subjunctive, so some grammarians do not consider it allowable in exemplary prose.)
Now in your example (perhaps somewhat counterintuitively?) I would say that the change from lambs to lions is not stated as the desired outcome of prolonged rising, simply because it is an exhortation. The speaker wants to say that this will be the sure outcome – and therefore the present indicative or the future exactum would be appropriate:
Surge atque iterum surge, dum agni leones facti erunt.
Note that you could also say eritis – since presumably the speaker is talking to the “lambs.”