The bug
Mobs without natural fire resistance which are swimming in lava cannot pathfind. You can see that they recognize their target, for example vindicators raise their axe, but they don't move at all. This does not apply to zombified piglins, wither skeletons, and blazes.
Reproduction steps
Create a 1 block deep pool of lava
Summon a Wither Skeleton in the lava and switch to Survival
✔ The Wither Skeleton slowly moved towards you; as expectedSummon a Vindicator with fire resistance in the lava
/summon minecraft:vindicator ~ ~ ~ {active_effects:[{duration:-1,amplifier:0b,id:"minecraft:fire_resistance"}]}
❌ The Vindicator repeatedly raises its arms for a short time but is unable to move towards you
Linked issues
relates to
Comments
Confirmed for 1.13.1.
Confirmed for vindicators in 19w12b.
Cannot confirm for fire resistant mobs in 20w09a. Fire resistant mobs will pathfind in lava, while non fire resistant mobs won't move.
I am unable to reproduce this issue in 20w49a. As stated above, fire resistant mobs will pathfind in lava, while non fire resistant mobs won't move and this is still the case.

What you are describing is the bug this report is about; I have edited the description and added reproduction steps to hopefully make that clearer.
Thanks for adding further details about this issue and helping me understand the problem overall. With that being said, I can confirm in 21w05b.

Can confirm in 1.19.4
In 23w44a
This issue relates to MC-104631.