Tomb of Levistus is an eldritch invocation for warlocks from XGtE, p. 57 (emphasis mine):
As a reaction when you take damage, you can entomb yourself in ice, which melts away at the end of your next turn. […] Immediately after you take the damage, […], your speed is reduced to 0, and you are incapacitated. These effects, including any remaining temporary hit points, all end when the ice melts. […]
I believe the intention is obviously that you are, well, “entombed in ice” and hence cannot move.
However, the spell Freedom of Movement states
You touch a willing creature. For the duration, the target’s movement is unaffected by difficult terrain, and spells and other magical effects can neither reduce the target’s speed nor cause the target to be paralyzed or restrained.
Clearly, Tomb of Levistus is a magical effect, so RAW I’d say you can still move. However, in my opinion, it makes no sense at all that you would be able to move and still gain all the other benefits from Tomb of Levistus, just because of one mid-level spell.
Are there any rulings/guidelines on similar cases / etc. that provide an indication of how to handle this situation? Or is it completely up to the DM how to handle the case?
You can move but not take actions.
The interaction is as stated in the question; Freedom of movement prevents tomb of Levistus from reducing the warlock’s movement. It doesn’t however, stop it from imposing the Incapacitated condition, which is simply:
An incapacitated creature can’t take actions or reactions.
Note that actions and movement are distinct things in 5th edition D&D:
On your turn, you can move a distance up to your speed and take one action.
It’s not unusual to hear people refer to using a “move action” in 5e, but that’s not how the rules are written; movement is separate from taking an action. Being unable to take actions doesn’t prevent a character from moving; conversely, being able to move doesn’t mandate that a character can take actions.
Losing all actions on your next turn is a significant tradeoff for the temporary hit points supplied by this invocation, even without the speed reduction.