I really wouldn’t know.
I stopped jailbreaking my devices a few years ago and all I can remember is that it took a very long time before jailbreaks came available.
Hopefully someone with more knowledge will come along and chime in soon.
It is hard to say when exactly iOS 11.4.1 jailbreak will be available but for sure it won't that far away. Now that Electra has found iOS 11.3.1 jailbreak toolkit and they jailbroke 11.4 beta version we have hopes with Electra teams to iOS 11.4.1 jailbreak come under. There are many predictions but we cannot say they will be true or not. So, all we have to do is just wait patiently for it to become real.
Wish if we have answer for this question. It is hard to say when , how or whom going to find out iOS 11.4.1 jailbreak toolkit. But we all are waiting for that. Anyway if you are intrested in downoad third party apps without jailbreaking then now there are online Cydia installer methods for that. All of these methods like Cydia Elite, are allow you to Cydia install by taking semi-jailbreak action on your iPhone. I used it on my iPhone X and still I didn't have any issue with that. Anyway, you shoul be careful with fake Cydia installer methods, as there are lot of them on the internet today.