The online translation on the LN hasn't been updated in years https://www.novelupdates.com/series/tensei-shitara-slime-datta-ken-ln/ (probably because it got licensed in English)
However you can buy vol. 1 in English (vol. 2 will be out in April and vol. 3 in August).
Kindle: https://www.amazon.co.uk/That-Reincarnated-Slime-light-novel-ebook/dp/B076H132D2/ref=sr_1_9?ie=UTF8&qid=1517507928&sr=8-9&keywords=reincarnated+as+a+slime
Paperback: https://www.amazon.co.uk/That-Reincarnated-Slime-Light-Novel/dp/0316414204/ref=sr_1_10?ie=UTF8&qid=1517507928&sr=8-10&keywords=reincarnated+as+a+slime
E-book (I can't buy Kindle books in my country but I can buy this version): https://www.kobo.com/ww/en/ebook/that-time-i-got-reincarnated-as-a-slime-vol-1-light-novel
Where can I read the light novel? I'very read the Manga and Web nivel but I wanna see wich one follows the original (light novel) more, so yeah.... (also Ima have no sleep if I don't find out what parts of the light novel they changed in the Manga and Web novel) ╥﹏╥