Cessna 560 departing LPC entered restricted area to the west.

Narrative

Unable to contact Santa Barbara or LA Center from ground for IFR clearance. Reviewed sectional and Runway 25 departure. Departure showed right traffic for Runway 25. C208 used for parachute jumping was not on field. I observed parachute jumping 45 minutes prior to departure. Parachute jumpers landed on east side of airport. The departure was to be a close left downwind departure. Climbing out VFR; TCAS 1 showed an aircraft above and southeast. As left turn was made; contact with LA Center to receive IFR clearance was informed aircraft was in restricted airspace and to call. Left turn continued to overfly west side of runway and proceed south. Clearance was received and remainder of flight was IFR. Flight departure should have been by the obstacle DP with vigilance toward east side of airport for parachute jumpers until radar contact and clearance received by LA Center . First flight into LPC; LA Center informed of parachute jumping in progress; jump airplane made one call; 'jumpers away at 7 thousand'; no other radio calls made. Concern prior to departure and no response from any aircraft on CTAF; we might have missed the call for jumpers away.