Are you asking how to evade lawful interception or how to comply with it without the legal process being side-stepped?
existance of corrupt law enforcement agencies
It would help if you provided some detailed specific examples that pertain of (un)lawful intercept.
Short answer:
There will always be those that try to take whatever shortcuts they can get away with. I've been party to these games many times. In attempt to answer your question and trying to not sound defeatist and to trying to force governments and corporations to follow due proccess warrants, etc... would require owning ones own datacenters and having armed physical security teams in hardened rooms behind ballistic LCD two-way mirrors and lawyers that can not be intimidated by fear tactics and that do not just perform check-box security and the like. This would also require not expecting a dependency on scratch each others backs mentality that many corporations ascribe to. Many corporations will permit governments to bend the law if they feel it will benefit them in the future and should they wish to get away with bending the law themselves. So I suppose the best one could do is own and operate all of their own datacenters including the entire physical properties and having redundant sources of power that governments can not easily subvert using intimidation tactics. Multiple circuits in the legal names of multiple shell companies that are not advertised in BGP on standby would also be required. It would probably also help to have multiple physical datacenters in multiple countries that are not in full cooperation with one another and force everything to be Active-Active N+2. Even then there are 3rd party services that could not be protected in this manor such as domain names, CDN's, DNS providers assuming you are not your own DNS and anti-ddos, certificate authorities and certificate transparency logs that could be legally compelled to exclude something. And then there is the issue of BGP filtering that could be imposed on such a hardened setup. So in conclusion one would need multiple datacenters under their full control, fearless people with integrity and services that do not depend on 3rd party services and in some way indirectly do not depend on public IP addresses associated with that infrastructure.
To my knowledge there are no corporations that provide what I just described. This would be getting closer to the territory of oligarchs and organized crime that could afford to build such a setup in my opinion. I doubt they would even consider wasting the money and would instead just distribute their sites to infected end-user hosts and infected servers/VM's using command and control nodes. Some may try to use "bullet proof hosting" and those are just shady resellers making false promises. They do not last long, their servers get seized and the ones that do last long are glowing honeypots.
I tried and failed to not sound defeatist.
