LAX Local Controller failed to issue traffic to a Runway 25R departure as a Runway 24L departure was making a left turn in front of the 25R traffic; traffic was issued by the Departure Controller.

Narrative

I approved Air Carrier X the LAXX6 departure from Runway 24L on a H210 vector departure for Local 2. Moments after LC2 called me and coordinated the H210 departure; I launched the Loop4 (CRJ7) departure from Runway 25R. As Air Carrier X was turning 210 degrees in front of the departing CRJ7 I shipped him (CRJ7) without issuing traffic. Although the course divergence was established; and I called the Departure sector to advise the RADAR Controller to issue traffic; I should have issued the traffic myself. When I inquired with the RADAR Departure Controller if everything was O.K; he said 'yeah' indicating to me that pilots did not complain. My assist was observing all this at the time. Recommendation; use of the placard (visual que) I removed the placard as soon as the other Controller told me that the cross-over traffic rolled. In fact; the aircraft did not roll for at least a few seconds; and by removing the placard; I misjudged the distance requirement. Thus; delay removing the visual que. Furthermore; when it appears that it's going to get close enough; then issue traffic.