In some ways, this is a surprisingly synergistic combination. It’s trivially easy to match the spellcasting scores of both classes up, and they are both short-rest, pointsbased spellcasting classes. Their play styles/party roles are similar enough that the biggest point of conflict is figuring out why you want both instead of just one or the other. There’s also enough overlap where the other question you’ll want to answer is why you’re willing to miss out on the higher-level features of one or the other in order to get the low-level features of both.
In terms of class feel and lore, this is an odd pairing. It can certainly be made to work, but you’ll definitely want to give some consideration to the specifics. Archetype choice will do an enormous amount to define the character and what makes them tick.
Pretty much any mix of these two will play similarly; you’ll have a pair of potent damage-dealing class features at your disposal and back them up with spells. Emphasizing one or the other is largely a choice of whether you want the squidgy, eldritch flavor of the warlock to be dominant, the mystical flavor of the elementalist takes the fore, or the two exist in balance.
[[Synergy Feats for Multiclassers#Elementalist w/ Warlock|Elementalist-Warlock chains and ideas]]