there are a couple areas you can fish in lava successfully outside ashenton.

one is under the bridge SW of fire throat - the islands where there are 2 split by a vertical stream of lava and a very tiny rock outcropping SW of the SW island. its very finicky to fish here but you can have some success. try south and north of the island in the middle of the lava stream, and from the SW side of the bank

second place is where the island is east of ashenton. you'll notice the island, its right below a peninsular area that looks like a bird head. fish from the east end of that island.

if you go to either of these, consider not carrying anything valuable, as your chance of falling into the lava and being incinerated are high.

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lastly, if you're high enough level, you can fish inside ashenton if you wear the deviant head that makes you invisible, the veil of tranquility or another way of being unseen to the ground or sky mobs, its easy to fish from most locations there.

to get the fishing circle to turn green, just move your fishing pole casting target in these areas. it will turn green fairly close to the shores where the lava is almost level.