Yes, I'm not sure on the difference between a lavatory and a slop sink. Will the slop sink be in the bathroom, or in a separate room?
If in the bathroom, and you call it a lavatory, and it's plausibly a lavatory, what you have now is fine. If it's outside the bathroom, and it's not plausibly a lavatory, then you aren't allowed to use it for horizontal wet venting. It's a regulatory distinction, perhaps based on the idea that the flow pattern from a lavatory will be different from other sinks, or perhaps without a technical justification.
If it's not a lavatory, then I gave a few options in the previous thread. E.g. the one below, where Green =1-1/2" dry vent, Blue = 2" drain, and White = existing pipes I erased. I routed the slop sink drain around the outside of the shower in order to avoid crossing the shower dry vent. But if you have room in the wall framing for the crossing, that would be a more direct path and avoid any additional concrete removal. The vented slop sink drain can connect anywhere except upstream of point A.
Cheers, Wayne
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