After several references to the Q Continuum, Star Trek: The Next Generation, and it's no mere coincidence that his appearances bookend the series. However, Q remains uniquely suited for the TNG ethos, and his character never really fit in with later series. Based on the recent appearance in Lower Decks, however, that looks to change.
Q first appeared in the TNG series premiere "Encounter at Farpoint," characterized as an alien similar to humankind's many trickster God myths. Q put the Enterprise crew on trial for the crimes of humanity, demanding they prove to him that their species deserves to exist. The episode channeled the spirit of Captain Jean-Luc Picard (Patrick Stewart).
Although de Lancie would reprise the role for a few episodes in later series, none of these Q appearances are as memorable or significant as his contributions to TNG. Q appeared in a few episodes of Star Trek while also offering a plausible reason for Q's renewed interest in humanity.
In the Lower Decks episode "Veritas," Q makes a welcome return in a cameo that sees the character in his original "Encounter at Farpoint" attire. He attempts to goad Ensign Beckett Mariner (Tawny Newsome) into matching wits with him, but she promptly shoots him down, telling him to "go find Picard." Q responds "Oh Picard! He's no fun. He's always quoting Shakespeare, he's always making wine..." — a reference to Picard running his family vinyard at the beginning of Star Trek: Picard. While this is possibly a continuity error, as the events being alluded to haven't yet happened when the Lower Decks episode takes place, it may actually be laying the groundwork for de Lancie to revisit his favorite "Capitaine." In addition to the fact that the Q cameo on Lower Decks predicts Picard's future, it also provides a reason for Q to return in Star Trek: Picard: because Picard is fun again.
season 2 is expected to feature Picard leading a rag-tag team of misfits on various adventures in space. This offers the perfect opportunity for Q to reappear in Picard's life — if only for a cameo similar to the one in Lower Decks. For the most part, Star Trek has moved past the more fantasy-inspired plots of TOS and TNG, and seemingly-magical beings are unlikely to have a role in the series going forward; however, Picard has demonstrated a willingness to celebrate beloved ideas and characters from TNG, and Q was such a significant character for Captain Picard's overall TNG arc, the sequel series would be remise to not include de Lancie's mischievous trouble-maker. Q has saved Picard's life more than once, and the former Starfleet captain just died and became reborn as an android — it's hard to believe that none of these developments would spark Q's interest.