A dead lich may be resurrected if its phylactery is also destroyed
When discussing whether true resurrection can raise a lich, there are 3 distinct cases that must be considered.
Undead/Not dead lich - cannot be targeted by true resurrection
You touch a creature that has been dead for no longer than 200 years and that died for any reason except old age. ... the creature is restored to life ...
True resurrection requires a dead creature to be the target of the touch. A lich is an undead creature, but it is not dead. Jeremy Crawford confirms this:
An undead creature is not dead.
It is thus not a valid target for true resurrection.
So, using true resurrection will only work on a lich that has been killed. The effectiveness of the spell in this case will be determined by the state of the lich's phylactery.
Dead lich, phylactery intact - cannot be resurrected
If you kill the lich (before destroying the phylactery) then use true resurrectionit likely will not be able to come back to life because:
A lich is created by an arcane ritual that traps the wizard's soul within a phylactery... where it forever remains.
A soul that is trapped forever in a container is not "free and willing" which means that the soul does not meet this condition of true resurrection:
If the creature's soul is free and willing the creature is restored to life...
Since it does not meet that condition, the lich cannot be restored to life by true resurrection while its phylactery remains intact and active.
Dead lich, phylactery destroyed - can be resurrected as non-undead creature
If you kill the lich (after destroying the phylactery) then use true resurrection it will return to life as as the creature it originally was.
Per the description of true resurrection (after errata):
If the creature was undead, it is restored to its non-undead form
Assuming that the soul is now willing after being freed from the phylactery this means that the (former) lich can now be resurrected to its non-undead form.