Yes, your sentence is fine and perfectly understandable.
But while there's nothing wrong with it, I'd say it's generally more common to use the present participle.
Compare these two:
I've just seen a lady who has just come out of the hospital.
I've just seen a lady coming out of the hospital.
Both versions are correct, but the second version uses fewer words.
In colloquial speech (if this is, perhaps, something we'd be saying to somebody on the phone), we tend to avoid additional verbs and relative pronouns if we can say the same thing without them.
Unless the action of leaving the hospital is one that takes a long time, the use of just in front of the first verb is all the emphasis that's needed to imply that the entire sequence of events has occurred only very recently.
Note that the emphasis of the sentence can change if the verb form is changed:
I've just seen a lady coming out of the hospital. [She wasn't in a hurry.]
I've just seen a lady come out of the hospital. [Its doors must be unlocked.]
In the first version, the present participle puts an emphasis on the action of the woman. But if the context of the narrative is talking about the status of the hospital itself (let's say it's a thriller and the narrator is somebody wondering if the hospital has been locked down yet), the second version is more a simple statement of fact about the situation itself rather than the woman.
Also note that the original version of the sentence could be used for intentional effect:
People say the place is haunted, and I have to agree. I've just seen a lady who has just come out of the hospital. She's trembling and pale as a ghost.
In this context, the repetition of just in front of this verb tense puts additional emphasis on the immediacy and mood of the situation.
Oddly, it's also possible for this to mean that you've seen this lady seconds ago, but she came out of the hospital an hour ago. Despite the second use of just, it can still be understood to not be as immediate a statement in terms of time as would be the other versions of the sentence. (The interpretation of just can be relative.)
So, both in terms of style and intention, the original version of the sentence might well be more effective than any of the other expressions. But if the immediate nature of both things is to be made explicit (without any ambiguity at all), and if further context doesn't relay that, I would use one of the rephrased versions.
