These emails (addressed to your LP site) successfully arrive at LP, but when you try to forward them to Spectrum, they always vanish? I suppose that could also be LP failing to forward them, rather than Spectrum not handling them (don't count on LP's diagnostics). I don't think either party would dare (in the US, anyway) block a gun-related site, but why would anyone block MarketWatch? Could either of these emails always contain something that looks like spam? If you haven't done so already, I think you're going to have to take this up with LP support (open a ticket) to see if they're blocking as spam outbound. If you're getting other email forwarded, it's unlikely that the entire LP server is blacklisted as a spammer. Can Spectrum tell you for a fact that they are receiving nothing for the forwarded emails (placing the problem with LP)? Finally, you've gone over your mail setup on LP and Spectrum with a fine-toothed comb, and there are no old remailers, filters, or forwarders that you forgot about?
If you can't fix it this way, at the least you can still receive them on your LP site, fire up T-bird to read them onto your PC, and autodelete them from LP. That should be easily done.