Abstract It is largely unclear whether genes that are naturally embedded in lamina associated domains (LADs) are inactive due to their chromatin environment, or whether LADs are merely secondary to the lack of transcription. We show that hundreds of human promoters become active when moved from their native LAD position to a neutral context in the same cells, indicating that LADs form a repressive environment. Another set of promoters inside LADs is able to "escape" repression, although their transcription elongation is attenuated. By inserting reporters into thousands of genomic locations, we demonstrate that these escaper promoters are intrinsically less sensitive to LAD repression. This is not simply explained by promoter strength, but by the interplay between promoter sequence and local chromatin features that vary strongly across LADs. Enhancers also differ in their sensitivity to LAD chromatin. This work provides a general framework for the systematic understanding of gene regulation by repressive chromatin. Highlights Two promoter transplantation strategies elucidate the regulatory role of LAD chromatin LADs are generally repressive, but also highly heterogeneous LADs can impede both promoter activity and transcription elongation Promoters vary intrinsically in their sensitivity to LAD repression