I would say, adapt the weight to what works for you. I used 3 different weights when doing Ironborn precisely because some exercises were not possible with the same weight as others. When a weight is not challenging you anymore, go up. Although that depends on your goal, strength or endurance or mass... I leave that answer to the experts here like HellYeah

Honestly, Lateral Raises are one of those exercises you should start with a very low weight so I'd advise you to go even lower until you can comfortably lift the number of reps.. Especially if you've never done them before and don't know proper form yet. I'd go even so far and say, if you're new to weightlifting, start with the lowest weights and learn proper form FIRST before lifting for reps and volume.
The simple illustrations in the programs aren't enough to learn proper form, look the exercises up, read what muscles are targeted and how to perform them, maybe watch a video, and then practise with low weights until you're certain you hit the right muscles.
Everyone is different, the recommended weight given in the program's description aren't a 08/15 solution for everyone. Some can start higher, some have to, and probably should, start lower.
If your form is correct and you can hit the required numbers of reps easily, go up on weights if you can. If you can't because you don't have any, perform the exercise slower and focus more on contraction of the muscles. But don't just do the same number of reps the same way with the same weight.

Anek I am humbled...

​​​​​​... ​but, I have nothing to add to lofivelcro expertise

With a 20lb dumbbell I keep the elbows bent, from the starting position db in front, circle the arms as if tracing a huge clock face keeping hands in front letting the shoulders do the work. With a lighter weight I lift straight from the side. Also have you tried doing single arm ? Dumbbells in my gym are 15 and 20 lbs no kg.

Now I am the one who is humbled...