Since you asked about timing, MECCG uses "last in, first out" game timing called a "chain of effects", which might be similar to some "stack" concepts but I don't know if it is similar to "the stack" you are talking about. In MECCG, cards or effects can be declared in response to each other and then they all resolve in order and uninterrupted from last declared to first declared. Furthermore, the effects of a dice-roll are declared with (and resolved with) the dice roll itself.
Declaring a "test" of a gold ring includes both the dice roll and the potential play of various special ring items depending on the dice roll. Playing a special ring is the actual (resolved) effect of the test. These actions are all declared together in the same chain of effects and then they will resolve together. Because of this timing, there is no way to declare Lobelia's retrieval-ability in the middle of an already resolving chain of effects. There is also no way to delay the resolution of playing the special ring item until a later chain of effects. The play of the special ring must happen, if at all, when the test resolves. If the resolved dice roll does not match a particular type of special ring, then play of the non-matching special ring is negated.
So, it's true that Lobelia cannot retrieve special ring items because such items are not "playable" at her site. But EVEN IF special ring items were playable at her site, she still could not use her ability to retrieve the special ring item after seeing the dice roll and then play the retrieved card as the tested ring -- the timing rules do not allow for this.