Andrew Sarangan wrote:
If you pass the VOR within 1/2 mile, I would consider that as 'crossing
the VOR'. The original poster was close to the VOR when he took off.
Hence I don't see a need to return to that VOR after taking off. Just
proceed to the next fix.

I agree with Andrew, but feel compelled to point out that this is only
true for an en-route clearance. If you were flying a DP which said
something like "fly runway heading to 1000, left turn direct Lancaster
VOR, the proceed on course", that would be a different story.

But, the OP didn't say anything about a DP, so I'm assuing that's not
what was going on here.