Lift chains also need to be checked / lubricated correctly.

What are the legal limits / requirement's on chain's & forks in your part of the world?

While some aspects of an IC forklift could be diy serviced there are other parts of the machine where you really need an expert to inspect / check them as if you get it wrong you could open yourself up to prosecution in the event of an accident.

Just two good reasons (there are others) to have an "expert" check it is to make certain the inching pedal adjustment is functioning properly & make any necessary adjustments or repairs before you incur any 'big check books" repair costs the other other is to check for excessive fork wear, especially at the heel of the forks too much wear (usually caused by dragging the fork heels on the ground) can cause major issuess - damaged product or personal injuries or worse.

I have no doubt about your ability to change the oil and filters, but one of the main reason we do PMs on forklifts is as much as is possible to see the future, is to have an expert look the truck over and catch potential failures before they happen.
as far as the intervals, grab the operators manual, and read it as if it was "gospel truth". it should tell you what to change, where the grease fittings are and what fluids to use.