"LS-4 posted" means: DOB couldn't get access, so mailed the owner a letter asking him/her to schedule an inspection.
To find out what hapened, I'd check every conceivable category in DOB's online listing for that property ... not just complaints/violations, but C of O, Actions (which often are _not_ in chronological order!), Permits, Plumbing, Electrical, et al. Relevant info often is tucked away there -- i.e., whether they were fined, filed a permit, corrected the problem, or if DOB decided the complaint was unfounded, so dismissed it.
If there's nothing at all but an LS-4, there's a chance that there was no followup, the complaint just fell into some black hole (or was "adminstratively" closed, which is pretty much the same thing), and it's still in violation.
For more detailed info ... the DOB site is searchable, and has tons of info re: inspection procedures, or you could check with DOB directly.