If there are more films in the Enola Holmes universe and they closely follow the books, then the character will not be getting a love interest.
The Nancy Springer novel series focused on Enola's mystery solving abilities and her family relationships with brothers Mycroft and Sherlock. Her ultimate estrangement from her brothers has largely to do with her desire to be independent, despite her young age. It makes sense, then, that romance is on the back burner for the character.
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The plots of the six novels is mainly focused on the mysteries at hand, the development of various friendships, and how the young female characters do not need to be beholden to anyone else.
In the fourth book, The Case of the Peculiar Pink Fan, Enola even helps her friend Lady Cecily avoid getting married against her wishes.
But, Lord Tewksbury (and Louis Partridge) have been getting a lot of attention online, so it wouldn't be too surprising if a potential film sequel diverged from the novels in order to continue including the character. If this did happen, it's unclear whether or not this would entail him becoming Enola's romantic interest.
A sequel has also not officially been greenlit at this time.
Enola Holmes is now available to stream on Netflix.