The short answer is — Lincoln does not go to SONA as an inmate. However, the longer answer involves a brief visit, a close call, and a major character swap.
In the Season 3 finale, Lincoln is captured and taken to SONA — but Michael orchestrates a swap. Lincoln is released almost immediately in exchange for Whistler. So while Lincoln enters SONA under guard, he is never an inmate. His total time inside the walls is minutes, not months. does lincoln go to sona