Just farm the quest on the map that has a counter of ???/250 at a difficulty your able to. Once you reach the 250 run the last quest and you can continue on.
The lions are basically an easier way to star-up your heroes as when you get them they are starred higher then the other materials you’ll have to raise and up-star. To up-star, you need to max level, and then give that unit ____ (whatever star level it is at 2=2, 4=4, etc.) of same star units and it will graduate to the next star.
Have a Montmorency at 3 stars and max level, got 2 phantasm units at 3 stars and a Mucacha at 3 stars, any level. Give Mont those units and she will become a 4-star. Rinse and repeat with higher number stars to eventually get to 6-star Mont.
Find characters you’ll use in your inventory and decide how much investment you want in them or if your going to replace them if something better comes along. Awaken is cheap, but skill enhance you should save for a core team until you can expand beyond a single catch-all general team.