Laser wakefield acceleration (LWFA) and its particle-driven counterpart, particle or plasma wakefield acceleration (PWFA), are commonly treated as separate, though related, branches of high-gradient plasma- based acceleration. Both have certain benefits and drawbacks, but in combination they might open a new path for generating ultralow-emittance electron beams from readily available laser sources. While LWFA can generate ultrahigh-current, highly relativistic electron bunches, the beam emittance is typically compromised by the strong plasma heating by the oscillating laser fields. By using these LWFA-generated bunches to drive a wakefield in a secondary, cold plasma, and employing cold injection schemes to provide a suitable witness bunch, we aim to generate ultralow-emittance beams in a small laser lab. We call this approach Hybrid LPWFA. I will present an overview of experimental findings that triggered this research, along with the first observation of such LWFA beam-driven wakefields, and their first application for accelerating an externally injected witness bunch. Finally, I will show recent results on the stability of LPWFA, and the properties of witness bunches generated by the first internal injection studies.