It's worth looking at the detect balance spreadsheet when thinking about homebrew race balance.
Intelligence +3 is too good
No race in the game has a +3 to a stat. This is too good because it can allow you to get an 18 in a stat for a starting character (using the standard array). You should make this intelligence +2 and add +1 to some other stat.
(The spreadsheet agrees with this: no race should have +3 to a stat. If you had a +2 and +1, the spreadsheet says it should cost 12 points.)
ray of frost and thunderwave are fine
There's precedent for creatures getting once-per-long-rest spells as racial abilities, and these spells won't be game-breaking. You might want to mention which stat will be used for the save DC for thunderwave (obviously intelligence, but still worth mentioning).
The spreadsheet says each of these should cost 2 points, for a total of 4 points.
animate dead is troublesome
The spreadsheet gives a cost of 3 points for this, but for this particular spell I have some worries. Characters using animate dead can be disruptive to a campaign (see, eg, this question). Someone playing with this race would need to check with their DM and make sure the campaign would still work with a group of undead servants following the party around.
Also, the animate dead spell either lets you create one undead servant, or maintain control over four of them; if a character can only cast this spell once per day, they'll only be able to have one undead servant at a time, unless they allow the previous ones to go temporarily uncontrolled while creating new ones.
Advantage on intimidate checks is fine
The spreadsheet describes this as worth 2-4 points depending on how common an intimidate check is.
(You described this as advantage on "sight-based" intimidate checks, but nearly all intimidate checks are made against creatures that can see you, so this is nearly equivalent to advantage on all intimidate checks.)
Some traits we normally associate with liches are missing
Normally liches are tremendously powerful undead wizards. They don't have to sleep, eat, or breathe. If killed, they regenerate from their phylactery. They have a great deal of arcane knowledge which they accumulated in the process of becoming a lich.
This race has none of those things. It doesn't even seem to be undead. That's not necessarily a problem for gameplay, but it might lead to misunderstandings -- for example if the player says "I hide underwater because I don't have to breathe" and the DM says "you do have to breathe" and the player says "I don't because I'm undead" and the DM says "this race doesn't say you're undead".
If you want to add all these traits, you can do that, but then we have to factor them in to the balance of the race.
The flavor of this character is alarming
How is this character going to integrate into the campaign world? How is it going to integrate into the adventuring party?
In most settings, NPCs react with shock and horror to the undead, and they especially fear liches since they tend to be super evil. Your lich race is explicitly called out as being usually evil.
When a lich character walks into town, do all the villagers run and hide, and then the city guard mobilizes to try to destroy the intruder? If not, why not? Does someone playing this character just have to negotiate an out-of-character agreement with the DM that NPCs simply won't notice the evil lich in their midst?
What about the other player characters? Why are they adventuring with a lich? Do they trust the lich? Does the lich trust them? If so, why?
I would suggest that you reflavor the race to be less evil and scary, but with your "terrifying visage" trait it feels like having a really evil scary character is the whole point of this race.
Most groups will probably say: "we're trying to tell a story about a heroic group of friends who right wrongs and thwart evils, and that group probably wouldn't be friends with a lich, so please don't play a lich character."
Overall, this race is valued at 22 points (assuming the +3 intelligence is changed to +2 and +1), and the spreadsheet says races should get 23-27 points, so what you have is a little bit low. Read over the spreadsheet and see if there's something else your race should have, like darkvision, or resistance to necrotic damage.
But you'll have to think carefully about the flavor.
