As with Mark, Luke's account emphasizes that Jesus would eat the Passover with His disciples, not merely prepare for it. In verse 15, He declares how great His desire had been to eat that Passover with them. His focus that evening as He sat with His disciples was on eating the Passover, not on being the Passover. He spoke of what He was doing then, not on what He would be doing later on the 14th.
His words also reveal that the eating of the Passover was to be before He suffered (verse 15). His crucifixion began at “the third hour” (Mark 15:25), about nine o'clock the following morning, and ended after “the ninth hour” (Matthew 27:46). Jesus obviously knew when Passover was to be observed, and “with fervent desire [He had] desired” to eat it with His disciples before He suffered. There is no indication He said this in reference to a meal the following afternoon or that He longed wistfully for the crucifixion to be put off until He could eat a late Abib 14 Passover.
The only conclusion is that He did in fact eat the Passover with His disciples that evening after the 14th had begun, prior to His arrest later that night and His appalling suffering, which began the next morning. These three accounts should leave no doubt that Jesus intended to, and in fact did, eat the Passover with His disciples at the beginning of the 14th day.
David C. Grabbe
Why Was Jesus Not Crucified as Passover Began? (Part One)