Hi!!!
It went well but was long!! I ended up doing it manually because I didn’t want to pay to do it and wanted to have control over it because we had A LOT of inventory. So the inventory, gift cards, customer info I transfered over. I found out after the fact that you can also transfer sales history but I didn’t know so didn’t do it… even if it was a lot of work I have absolutely 0 regrets and it was so worth it. I do not miss lightSpeed and never want to go back. We didn’t have a good 4 years with them. Shopify is much much better. I also created our new website in Shopify and then created our items online anew.
So everything can be transfered except for store credits. But I printed a sheet with all the store credits we had left over and keep it at the till to use manually.
There is a few apps you can pay to help do the transfer OR you can also pay an agency to transfer it all for you. For us it was a choice and I just didn’t use them! If you talk to Shopify support they will give you some names. 
I hope that helps!!
If you have any more questions let me know!! Just email me
Have a good day and good luck with the switch over!!!