Some TMNT stuff really isn't for little kids.
In the IDW continuity, Harold Lilja's laboratory is the facility that Harold used frequently during his dealings with the Turtles, after he was forced to abandon his previous facilities to hide from Baxter Stockman. It was located in an old industrial building that Harold had redesigned according to his needs, such as installing a cooling unit for his computer servers.
This laboratory was where Harold could frequently be found, and was where he developed many of his technological achievements, including Metalhead and Nobody's exo-suit. He kept it under constant security surveillance. Donatello first visited the laboratory during the City Fall arc, when he was asking Harold for equipment to help rescue Leonardo from the Foot Clan.
Upon his return from the O'Neil Farm in Northampton, Donatello again visited the lab, where Harold had been developing the Metalhead robot in order to keep his lab safe from any enemies he had, such as Baxter Stockman. The robot malfunctioned, and the lab suffered severe damage as a result.
The lab became a vitally important location when Donatello enlisted Harold to build a functioning teleporter, in the hopes of teleporting to Burnow Island and defeating Krang. This led to the groundbreaking machine being located in Harold's lab, where it was used both by the Turtles and the Foot Clan to access Burnow Island. It was also the location where Donatello was mortally wounded by Rocksteady, and where Fugitoid Professor Zayton Honeycutt barely managed to save his life after transferring his consciousness into Metalhead. Donnie's battered and comatose body was put on life support first inside Harold's cooling unit to slow his cell metabolism, before his life support rig was transported back to the lair beneath the church for long-term care.
The lab was also the place from which Harold was later abducted by the Street Phantoms, acting on information intentionally and unilaterally leaked by Splinter, the Turtles' father who had become new leader of the Foot Clan. After being used by Splinter as an unwitting pawn in such a manner, Harold cut all ties with him, the Turtles and their other mutant and human friends alike, and reunited and again went into hiding along with his ex-wife Libby Meitner.
However, the abandoned lab was revisited by the Turtles during the Metalhead 2.0 arc, in which Metal-Don went to the lab while confused and wracked with emotional pain. They learned that he had used his weapons to blast the lab and its contents, before discovering a hitherto-secret room where Harold had left a larger, more powerful Metalhead chassis.
Donatello has since increasingly used the lab as a second larger laboratory for his own needs, and its location has since also become known to Baxter Stockman (whom it was initially intended to remain hidden from) since his détente with the Turtles and his work partnership with April O'Neil at TCRI. The lab is still generally referred to as Harold Lilja's lab, even during the long period after Harold cut ties with the Turtles and was no longer shown to visit.
But since Harold and Donatello reconciled in the Donatello Macro-Series issue, not only did Harold start regularly visiting the lab again, but Libby would visit as well to work with Harold and Don.
The location of Harold Lilja's laboratory is marked on the Zones of Control maps which begin publishing in City at War, part 1. It is roughly located at coordinates 40°45'22.08"N, 73°57'48.12"W, situated on the north side of 54th Street on a block located east of First Avenue and west of Sutton Place near the East River facing Roosevelt Island. In real life, these coordinates correspond to St. James's Tower Condominium, a residential high-rise.