generally you can use the same principles/methods for measuring the ablation threshold for ablation in a liquid than for ablation in air, but you must more carefully control the experimental constraints.
If you are using a laser beam with a spatially Gaussian intensity distribution, then I would recommend to you the so-called D2-method that was published first by J.M. Liu in 1982, see
Article Simple technique for measurements of pulsed Gaussian-beam spot sizes
The essential idea would be that you first immerse your sample in the liquid, adjust the sample surface in the laser focus plane and then irradiate the surface with a fixed number of laser pulses N (I assume here that you do not use a cw-laser) per spot, with all other parameters (such as pulse duration) being fixed - except the laser pulse energy: for each fresh sample spot, you are increasing the laser pulse energy (E), best by a fixed factor. If you chose the range of pulse energies in a good way, you are creating a series of separated ablation spots at the samüle surface. This spot series can then be evaluated e.g. with a good optical microscope, where you measure the diameter (D) of the ablation craters for the entire series.
If you then plot D2 vs. ln(E), you can determine from a least-squares-fit of the experimental data to a simple model of a Gaussian beam presented by J.M. Liu (see above) the Gaussian beam waist radius w0 and the ablation theshold energy Eth. That threshold value is valid for the value of N that you had selected (while w0 should not depend on N). Since the laser pulse energy and the fluence of a Gaussian beam are related to each other, you can easily calculate then also the ablation threshold fluence Fth for the given N.. Usually Fth(N) decreases for increasing N, an effect that is generally called "incubation". It may have different physical origins, depending on the irradiated material and laser...
This D2-method has the intrinsic advantage to evaluate w0 exactly ate the sample surface. But you must take care that the presence of the liquid does not disturb the measurement. For ultrashort laser pulses this may occur through the Kerr effect. Or it may disturbed by gas-bubbles created by the pulse and being present when the next laser pulse arrives to the scanario. So you may reduce the pulse repetition rate - or ideally use a single laser pulse. But then your samples should be quite smooth that you can easily see the ablation craters. Best make the least-squares-fit close to the ablation threshold since at high pulse energies/intensities the mentioned effects may significantly disturb.. Also it is beneficial to use a thin liquid layer above the surface only.
If you are using a closed liquid confining cell with windows for the laser radiation, then you should consider the Fresnel reflectivity of all interfaces in the beam path before reaching the sample, since these reflections reduce the amount of pulse energy reaching the liquid/sample interface. If you have no windows, then you may just consider the Fresnel reflectivity of the air/liquid interface. An example for a liquid confining cell is given here
Article Plasmonic formation mechanism of periodic 100-nm-structures ...
Complementing the contribution of Prof. Dr. Bonse, there is also a alternative method that can be employed to this purpose. It is one more option you can try and check if it fits well to your needs.
D-Scan measurement of ablation threshold incubation effects for ultrashort laser pulses