  We develop a tool for the analysis of stochastic gravitational wave
backgrounds from cosmological first-order phase transitions with LISA: we
initiate a template databank for these signals, prototype their searches, and
forecast their reconstruction. The templates encompass the gravitational wave
signals sourced by bubble collisions, sound waves and turbulence. Accounting
for Galactic and extra-Galactic foregrounds, we forecast the region of the
parameter space that LISA will reconstruct with better than $\sim 10\,\%$
accuracy, if certain experimental and theoretical uncertainties are solved by
the time LISA flies. We illustrate the accuracy with which LISA can reconstruct
the parameters on a few benchmark signals, both in terms of the template
parameters and the phase transition ones. To show the impact of the forecasts
on physics beyond the Standard Model, we map the reconstructed benchmark
measurements into the parameter spaces of the singlet extension of the Standard
Model and of the classically conformal invariant $U(1)_{B-L}$ model.
