How should I convert this character's level and stats into a CR?

Dale's answer seems mostly right, although some rounding here and there might have been made. To replicate in a full answer:

The guidelines are in DMG p. 274, but there are lots of more details in p. 275 onwards. Do note that these guidelines are known to be not completely accurate with the CRs from actual published monsters.

For more complicated cases, we split the Defensive CR and Offensive CR.

Defensive CR

This is calculated based on HP and AC. You start by finding the HP in the table, as you did: CR 4. Then, for every 2 points of AC higher than the AC for that CR (which would be 14), you increase the CR by 1. So +2 CR here, for a total CR of 6. The +5 prof bonus does align with the AC, so that should be fine.

Offensive CR

You find out the maximum damage output you have in the three first rounds. I will trust Dale's calculations that it should be around CR 13, or at least CR 12. Again, the bonus to hit is +10, compared to +8 for that offensive CR, so we increase by 1, to 13-14.

Average CR

Averaging it will get you CR 9 or 10. As mentioned in Dale's answer, however, this "monster" has a considerable awkward balance, with its offensive CR being way higher than its defensive CR. This is actually known already: player characters are not very balanced "monsters", because they have inherently way less HP, possibly considerable higher armor, and deal way more damage, especially considering burst damage (which, by the way, Warlocks are known to be quite good at, as well as Paladins).

Most of its damage is also concentrated in a single hit, dealing 1d8 + 6 + 6d8 + 1d6 in one attack. Since monsters usually have high HP, this is not a problem, but against player characters, this could easily knock a PC in one hit. When that happens, the CR may be adjusted further, as is the case with the Ogre.

For that reason, most NPCs that mimic character class concepts are still quite different from actual PCs. The Spy has Cunning Action and Sneak Attack, but also has Multiattack, same as the Assassin. If your intent is to use NPCs that look like characters with a class, you may have more success finding them in the NPC section of the Monsters Manual. In particular, the Archmage is a 18th level spellcaster which is translated into a CR 12 monster, so CR 10 for a 16th level character is not too far-fetched. Although the Archmage does have ways to boost its defensive CR, such as Stoneskin, Magic Resistance and resistance to Damage from Spells.

But there is more

The DMG from what I could see also doesn't include how attack riders such as knocking the target prone might affect CR which to me seems as though it should be considered.

Pages 280 and 281 include monster features, expanding on Step 13 found in pages 278 and 279, on how to take into account some common monster features. For example, Pack Tactics, which may provide advantage as often as your attacks against a prone target, is translated as +1 to hit. With Create Undead, the character also would likely represent a more dangerous threat than the CR indicates, as it could raise an army of undead before fighting.

Furthermore, monsters like the Shadows, Specters¹ and the Intellect Devourers can be tricky for their CR, and balancing encounters is usually more appropriate, from my experience, than trying to balance monsters.

Page 283 of the DMG also describes how to create Monsters with Classes, denoting some major differences, as for example the number of Hit Dice.

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Alternative ways of computing CR

My second link is to this website: http://blogofholding.com/?p=7338. It provides a very nice statistical analysis of CR.

We can reverse engineer the formulas it found in order to check what CR seems more likely.

$begin{equation} AC = 13 + frac{CR}{3} end{equation} $

Gives us a CR of 15.

$begin{equation} D = 5 CR end{equation} $

Gives us a CR of around 15 or 16 as well.

$begin{equation} Hit = 4 + frac{CR}{2} end{equation} $

Using the +11 to hit, CR 14.

Then, the problem is: the HP should be three times the Damage, so, around 240 HP here. However, with only 120 HP, that would be around CR 8, something completely out of how monsters are usually designed. So, to reiterate: if you ever plan to use such a character as an encounter against a party, you may need to tweak some of these attributes in order to make it more balanced.

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¹ Fun Fact: Out of like 10 times I put a Specter against a party of 1st level characters, I think I killed a character at least 5 of these times, simply because for most 1st level characters, actually losing 3d6 points of maximum HP means death, so if they take a hit and fail the Con ST, they are dead.

DMG p.274

Defensive CR

1. Hit Points = 119.
2. From Monster Statistics by Challenge Rating Table: CR = 4
3. AC = 18. Expected AC for a CR 4 monster is 14. This is 4 higher than expected so adjust CR up by 4/2, so CR = 6.

Offensive CR

1. The best 3 round combination is (other combinations come close and offer more front-loading but I think this is the highest overall total in 3 rounds):
   1. Bonus Action: Hex, Action: Rapier+1 with Hex and Eldritch Smite (50hp). Total: 50hp
   2. Action Surge: Finger of Death (65hp), Action: Rapier+1 with Hex and Eldritch Smite (50hp), Bonus Action: two-weapon fighting Rapier with Hex (14hp). Total 131 hp.
   3. Action: Rapier+1 with Hex and Eldritch Smite (50hp), Bonus Action: two-weapon fighting Rapier with Hex (14hp). Total 64 hp.
   • This is a total over 3 rounds of 245hp or 82 DPR.
2. From the table: CR = 13.
3. Most of this damage comes from attacks so +11/+10 to hit is at least 2 better than the expected +8, so CR = 14.

Average CR

The average of 6 and 14 is 10, so CR = 10.

However, this monster is a glass cannon and can deal a lot of damage in the first 2 rounds. Given that a 'squishy' 10th level PC might only have hp in the mid-50s, targeting a wizard/sorcerer in the early will almost certainly render them unconscious and may kill them outright. Even 'tanky' PCs could be rendered hors de combat very quickly. Heaven help the party if the warlock surprises them. Of course, after the first 2 rounds, the warlock's damage potential collapses.

As such, this monster may warrant a higher DC - this is a common problem with monsters that have wildly different offensive and defensive CR.