In a nutshell:
You carefully construct a public "you" for whom all of those ventures make sense. From hobbies/passions to defining moments, you engineer the story of "you".
Buying into Tech: it's your passion!
Fortunately for you, Silicon Valley has brought the world a string of high-profile tech billionaires that sink their money into ambitious projects out of passion. All those private space companies are a great example, and education is in the news all the time at the moment, but don't discount the forays into humanitarian aid, disease eradication efforts, etc.
Use this as your reason to get into advanced tech beyond the robotics/automation/communication that make sense for your business already. Think back to what inspired you when you grew up, and tweak that story to fit your target tech. Practice speaking about this with your most trusted advisors, until it sounds natural and you can express the feeling (think of your real invention/inspiration and you'll radiate that passion).
Buying into PR/Lobbying: you had a defining moment!
This is the hardest one, as you need to plan, prepare and execute one or more events in your life, without that being detected when reporters inevitably start digging into your life and background.
You'll need some tragic event that made "you" feel it could have been prevented if only some law/policy/public opinion were different. "You" then set out to make that change by hiring a PR Company etc.
If something tragic already happened in your personal life that fits the bill, make full use of that. Uncle got shot in a robbery? Sick parent got bankrupted by hospital bills? A friend got assaulted because of their (...)?
Of course, odds are that nothing quite so useful happened... yet. Time to prepare something of your own then.
Note: Depending on your morals, arranging for a personal tragedy could get very ugly. I'm going to assume you reject the option of harming innocent people to provide your defining moment (which would be a defining moment of a very different nature) and will pick a relatively harmless option as example.
Let's go with a popular celebrity option. "You" and your wife/girlfriend want children, but somehow can't have any. So you were working in secret to adopt some photogenic child from a politically and/or geologically unstable country. "You" now feel personally connected to that country and want to improve its lot, so your start supporting NGOs and set up a lobbying company for that.
Buying into international organizations: yay! a natural disaster!
This is preferably a follow-up to your defining moment: "you" feel connected to the people in (location of the disaster) and your conscience doesn't allow you to stand by and do nothing. So you rashly buy up whatever looks useful, send the people over there to help and... fail miserably.
You will be shocked and disappointed that your idealistic intervention didn't achieve its goals. After some public soul-searching, you will start repeating to whomever will listen that it was due to not being properly prepared and not having enough local people with language skills and expertise. You vow to not wait for the next disaster and start laying the groundwork right now, establishing a network of education experts and schools.
Note: Muscling in on post-disaster rescue efforts will result in a clash with existing NGOs. Some may even see you as competition. The initial backlash is helpful for your soul-searching/mea culpa/fixing-it story, but after that you want to play nice with them, as you will want to both recruit their experts for more authority as well as place graduates from your schools into their ranks, to gain more influence in later stages of your plan.
This kind of story should frame all your major acquisitions into a narrative that makes sense to people and doesn't invite undue scrutiny.
The minor excursions from your field of business can be adequately covered by business practices that have well-known precedents. Google with its many employee-driven side projects is a great example. Amazon can't stop itself from trying a new line of business the moment it threatens to become profitable.
Need an excuse for a dozen lawyers? Get yourself into a patent lawsuit.
Edit: as mentioned in other answers, diversifying is a valid business strategy in itself, but only if there's a profit to be had (or positive PR), limiting its applications.
Finally, some things you don't need to do yourself. Extend your network and support friends and business partners in their ventures. Learn to play Golf, put money in some investment funds and then invite both the investor and one of your intended recipients to a game or two. They'll get the hint and money will end up where you want it, with you having any hand in it officially.