Date: 201903
Local time of day: 1801-2400
Location: LAX.Airport, CA
Flight conditions: VMC
Weather elements / visibility: 10
Light: Night
Aircraft: Learjet 55
Operator: Air Taxi
Operating under: Part 135
Flight plan: IFR
Mission: Ferry / Re-Positioning
Flight phase: Initial Climb
Airspace: Class B LAX
ATC / advisory: TRACON SCT
Second aircraft: B737-800
Reporter organization: Air Taxi
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Instrument; Flight Crew Commercial; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Human factors: Workload; Distraction; Situational Awareness
Second reporter function: Pilot Not Flying; First Officer
Anomaly: ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Weather / Turbulence
Detector: Person Air Traffic Control; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Contributing factors: Human Factors; Procedure
Primary problem: Human Factors

Narrative: We were cleared for takeoff on 25R at LAX behind [a B737-800] as soon as he rotated. I knew we would be off before his takeoff point. I did not know he was going to the same fix as us; DOCKR. We were climbing to 3;000 feet to DOCKER; doing 250 knots when we encountered moderate to severe turbulence. We were then trying to turn left to 236 degrees per ORCKA2 Departure. I was trying to maintain control of aircraft; jockeying the throttles forward/back trying not to go over 5;000 feet. I was flying on my instruments when I saw aircraft tail lights out of my left peripheral vision and saw the 737 that took off in front of us about a mile from us. At that moment; the Controller said do you have the aircraft in sight at 11 o'clock and 1 1/2 mile? We replied affirmative. He said maintain visual on that aircraft. We had caught up to him. While maintaining visual with him and thinking about what to do next; the Controller said maintain 250 knots. So I looked back inside and saw that we were in a left bank; because I was flying visual on him out over the ocean (no reference visually). I corrected my heading by turning right 10 degrees when the Controller hurriedly said fly 240 degrees. Then Controller said climb to 12;000 feet.At this point; we were decompressing from the [wake turbulence] and a little distracted by the event. We were in the climb when Controller said 'Left turn 020'. We read back '020.' Controller said 'Left turn.' We said 'Left turn 080.' He did not correct us. Shortly after the Controller said; 'When able; direct KLIPR'. We read back 'When able direct KLIPR.' We were still bothered by what happened; while [programming] direct KLIPR. Before we were able to turn direct KLIPR; the Controller started asking us about what we did coming off the runway and about going to DOCKR and afterwards; what heading we were flying; etc. We were then talking about what happened between each other. We tried to answer him in this conversation understanding that this is being all recorded and inadvertently did not turn to KLIPR. Then he spoke hard to us for not going direct KLIPR and told us we had a possible pilot deviation.We should have not been cleared for takeoff that close to an aircraft slower than us going to the same fix. We did not know we were going to the same fix. Then the Departure Controller allowed us to get too close to that aircraft; we were flying on instruments. The controller started a conversation on the frequency about the event as if it was our fault; and asked us about what we did 2 minutes ago; and we; knowing that it was being recorded; had to discuss it before replying; while we were to be navigating. He distracted us from making that turn and navigating.


Second narrative: [Report narrative contained no additional information.]


Synopsis: Learjet 55 flight crew reported a track deviation occurred following a wake turbulence encounter in trail of a B737-800 departing LAX.