A321
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Situational Awareness
Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Flight Crew Returned To Departure Airport; Flight Crew Landed in Emergency Condition
Aircraft; Weather
Weather event departing from DFW on climb out on vectors out of around 12;000 AC (Aircraft) was hit by lightning on left side; left engine shut down; but spooled back up; then within seconds RT engine was struck by lightning AC lost radar. We [advised ATC and] requested vectors back to DFW. Weather was bad on climb out in all quadrants; departures should have not resumed so quickly. Wait until weather had moved further from the area before resuming departures.
Departing DFW climbing through 13;000 [feet] we enountered a suggested lightning strike. I remember seeing Eng N1 drop then another strike happened then I noticed Eng stall on ECAM.  I initiated a level off and the Capt requested a lower altitude and [advised ATC]. We also asked for vectors due to radar no longer working. During level off I noticed Eng relight and both engines stabilized. We leveled at 12;000 [feet]  between a cloud layer to assess situation. I suggested we return or divert. Capt was concerned about going back to DFW due to weather. After further review and weather ahead and no radar;  we received vectors north to return to DFW as per ATC. We returned to DFW with no further incidents. We were on hold for weather and ATC asked if someone wanted to path find a route through weather due to radar depicting lower returns from storm. Aircraft left and reported good ride then ATC starting releasing all aircraft. I didn't believe storm was far enough but with report of ATC and first aircraft reports we left. Storm was reporting green on radar and lightning just caught us.ATC allowing more space of weather from an airport.
Air Carrier Flight Crew reported Lightning strike during climb.