To clarify, a cancel is preformed by executing a move during another as to cancel the recovery of the first move into the second.
e.g: cr.mk xx Hadouken
A link is preformed by executing a move after another has finished and while the opponent is still in hit stun. A link is usually denoted by a comma.
e.g: cr.mp, cr.mp, cr.hk
The combo you are attempting, cr.lp xx cr.lp, cr.lp xx Hadouken, allows you to either cancel or link the first two jabs together; however, the second and third jab must be linked in order to cancel the third into the Hadouken. This requires you to delay your input for the third jab until the animation for Ryu’s second jab finishes.
It will take some practice to get used to, but after awhile it will become second nature.