By looking at your leg lifts I can tell with quite certainty if you have a good press to handstand or not. 

Both leg lifts and the press to handstand rely on the same key principles.
They rely heavily on hamstring flexibility, on hip flexor strength and coordination.

I was lucky as my coaches pushed me to develop all of these things at a young age.
Being very good at leg lifts helped me understand a lot about the key principles of the press to handstand, about precise technique and about which muscle to engage in which moment and which direction. 

I honestly always found the press to handstand quite fascinating because of its complexity. The press to handstand really shows how fascinating the human body is and how everything is connected to one long chain.

A press gets significantly easier and more efficient if you can compress well. If you can fold in half you don’t have to lean your shoulders as far towards the front in order to get your weight on top of your hands. This means you can be more efficient with your shoulder muscles and don’t have to invest as much strength. Additionally, your wrists won’t have to bend as far protecting them from injuries.

Leg lifts are similar in this extend. If you can fold in half you can get your feet all th way up on the bar without having to involve your chest muscles. In an ideal world you will be able to lift your legs using the hip flexors only almost all the way up.

The longer you can keep your body or in other words the less you have to lean the more efficient the movement gets and the more reps you can do. Now your argument might be that you are not interested in doing more than 1 press anyways and I don’t blame you but hear me out.

More efficient means less pressure which means healthier and this is exactly what we should all be striving for. We love what we do. By making things healthier we can do things over a longer period of time being able to do the things we love until a high age staying happy longer.

Now in order to get the feet up on the bar without rolling the upper body and engaging the chest muscles to close the shoulders we of course need lots of hamstring flexibility but we also need coordination. This specific mind muscle connection does not come easier. Developing it will take quite some time. Whilst you have to engage your hip flexors to reduce the hip angle you also have to engage the lower back muscles to pull the hips into an anterior pelvic tilt. Even if you are not able yet to arch the lower back whilst engaging the hip flexors you have to engage it nonetheless as your lower back would otherwise simply round.

A good way of practicing this is by placing your feet on a box in an L handstand and simply swapping between a posterior and an anterior pelvic tilt. This works exactly the same way when hanging from a bar.

Now whilst the movements and engaged muscles are the same there is one key difference between the anterior pelvic tilt in the press to handstand compared to the anterior pelvic tilt in the leg lifts. Since your body is changing orientation from one to the other gravity is pulling you in different directions.

In the press to handstand you have to lift your hips upwards and rotate them against gravity into the anterior pelvic tilt. When doing leg lifts on the other hand gravity is helping you with the anterior pelvic tilt. Now again this is only the case if you do have enough hamstring mobility to take advantage of gravity here.

Practice your leg lifts focusing on actively pulling your hips into an anterior pelvic tilt in order to improve compression strength, coordination and mind muscle connection. Improving details of the press to handstand takes time. These changes and advancements do not come quick or easily but with a bit of patience and a whole lof of focus you will get there guaranteed.

Stretch

Work on your hamstring mobility. The problem is that your active flexibility will never be better than your passive flexibility. This means that you can never lift your legs further than you can reach towards the front folding in half when sitting. Losen up your hamstring muscles. The less resistance they provide when piking the easier your leg lift will becomes. When ever you work on your hamstring flexibility make sure you are well warmed up and to focus on form. Do not round your back when you lean towards the front. Instead start by arching your lower back and switching the hips into an anterior pelvic tilt before pulling the belly button towards the front. The goal is not for the forehead to touch your knees but for the belly button to touch the toes. Use yoga blocks or chair in order to support your arms and to place yourself in a healthier position.

Build the needed strength

To get your legs up we need the obvious: We need hip flexor and core strength. Yet we also need the not so obvious. We need gripping strength. 10 leg lifts will take you around 30 sec so if you can not dead hang for at least 1min you will get in trouble.

Incorporate some dead hangs at the end of your workouts and start training your core with laying, sitting and ultimately hanging leg lift progressions.