I mean, this hike is a classic and everybody has to do it when they are in Cape Town. The hike takes about an hour to 1.5 hours and is not crazy difficult. Plus, since it's so popular, you can also do sunrise or sunset hiking here and will still be around people (still: don't hike alone!). I personally prefer the sunset hike because after sunset, if you are quick, you still have light for most of the way down whereas you start the sunrise hike in pitch darkness. But that's just my personal preference ☺️
Even though the hike is not crazy challenging, I recommend you do it in workout gear. I see a lot of tourists in sandals and it's not great. Also, I don't recommend sleeveless shirts since there is not a lot of shade and the South African sun is strong!
There is a part of the mountain where you can climb up some stairs and chains but you don't have to. You can also take the slightly longer route around – that one is also suitable for children I would say.
If you do decide to hike in the morning, I really recommend you bring a headlamp and go in a bigger group because there will be less people around than for the sunset hikes.
There is a designated parking area here: https://maps.app.goo.gl/HAPdvMiUVZtwrvHh6.
Note that you are not allowed to fly your drone on Lion's Head, even though you will see a lot of people doing it. But please, be mindful of the environment and wildlife and don't do it.
The same goes for Wally's Cave: You might have read about it but its currently closed for public, nature needs to regenerate and the paths are closed because of erosion. So don't be one of those people that disrespect the rules.