We demonstrate a laboratory-on-chip that combines micro/nano-fabricated features with a Convex Lens-Induced Confinement (CLIC) device for the in situ analysis of single cells. A complete cycle of single cell analysis was achieved that includes: cell trapping, cell isolation, lysis, protein digestion, genomic DNA extraction and on-chip genomic DNA linearization. The ability to dynamically alter the flow-cell dimensions using the CLIC method was coupled with a flow-control mechanism for achieving efficient cell trapping, buffer exchange, and loading of long DNA molecules into nanofluidic arrays. Finite element simulation of fluid flow gives rise to optimized design parameters for overcoming the high hydraulic resistance present in the micro/nano-confinement region. By tuning design parameters such as the pressure gradient and CLIC confinement, an efficient on-chip single cell analysis protocol can be obtained. We demonstrate that we can extract Mbp long genomic DNA molecules from a single human lybphoblastoid cell and stretch these molecules in the nanochannels for optical interrogation.