How you lubricate the steering is mainly a question of what lubricants you have, and how you like to work. You can get good results with an oil can, but you'll have to repeat the job more often than you might wish. I think a ride-on that is used privately rather than commercially, and stored in a dry shed, could get by very well can-oiled with clean engine oil if you oil it at least each third time you use it. If you insist on storing it out in the rain however, you will need grease to protect it when it isn't being used - and lubricating a simple machine that has no grease points, with grease, is dirty and tedious. If you were using your Greenfield commercially, I'd suggest a straight gear oil (SAE50 to 90, not an EP version) applied daily. You need a decent oil can to apply gear oil, cheap oil cans aren't up to it.
With a bit of practice I'm guessing you'll be able to lift up and support the front of the machine, working the steering from side to side as you lubricate each part. The oil will penetrate the king pin pivots better with the weight off the suspension. Don't forget the steering shaft and mechanism: oil each pivot.
Having said all that, some of our experienced ride-on owners will have worked out their own, undoubtedly better, solutions.