Maybe this is a good question for the lawyer's thread: what percentage of LWOP sentences are appealed?
(ETA but in answer to your question, I have heard relatives of murder victims say, yes, LWOP is a relief because appeals aren't automatic and aren't usually covered in the media unless they are successful.)
California, at least, has a Public Defender's Office, Appellate Division, that may take such a case. Or the convict can hire an outside attorney, represent himself, or rely on another inmate who has used his prison time to teach himself the law.
As katiecoolady implied, appeals are not heard in front of juries and there isn't the same push to "humanize" the victim by displaying his/her loved ones. So surviving victims really don't have to attend every appeal, at least as I understand it.