So, I'm building a lich boss for my players to fight. But instead of wizard spells, I'm instead trying to equip it with warlock spells due to the lich's background. Problem is, I'm having a hard time pocking the best spells to challenge my players. Any suggestions?

Also, I am using spells from the Fiend and Undead patrons as well for the same reasons.

What level characters are in the party?

Depending  on party lv but I find 1. armor of agythist  2.arms of Hader  3.hex and  hellish  rebuke  are  pretty  good  to   especially  aginst  malee fighters dumb enough  to go into melee  range   I once did over 200 points  of damage  to a fighter   and I did it with armor  of  agythist  hellish rebuke ,hex &Eldtrich  blast with only 2 lvs of warlock   and 18 lvs of wizard .   

Certainly use those spells as flavorful cornerstones, but a lich is not a wizard or a warlock. Those are PC classes. A lich is a monster and as such it can cast whatever spells you damn well decide it can cast, including spells from any class list as well as those that PCs can't, like an advanced Hunger of Hadar that's a 60-foot cone or does 2d6 extra damage.

But the key words here are "to challenge my players." We can't really answer unless we know what your players are capable of. Some groups have a lot more trouble with certain spells than others.