A monolithic lab-on-a-chip fabricated by femtosecond laser micromachining capable of label-free biosensing is reported. The device is entirely made of fused silica, and consists of a microdisk resonator integrated inside a microfluidic channel. Whispering gallery modes are excited by the evanescent field of a circular suspended waveguide, also incorporated within the channel. Thermal annealing is performed to decrease the surface roughness of the microstructures to a nanometric scale, thereby reducing intrinsic losses and maximizing the Q-factor. Further, thermally-induced morphing is used to position, with submicrometric precision, the suspended waveguide tangent to the microresonator to enhance the spatial overlap between the evanescent field of both optical modes. With this fabrication method and geometry, the alignment between the waveguide and the resonator is robust and guaranteed at all instances. A maximum sensitivity of 121.5 nm/RIU was obtained at a refractive index of 1.363, whereas near the refractive index range of water-based solutions the sensitivity is 40 nm/RIU. A high Q-factor of 105 is kept throughout the entire measurement range.