A lot of questions, but since they are related, we go on:
A spectral line is determined by a particular transition in an atom or molecule. In reality, this line isn't infinitely sharp, but has a small distribution about the resonance frequency as a result of a few things. This distribution will have a lineshape, e.g., Gaussian, Lorenztian, Voigt, etc. My first question is: is each spectral line, corresponding to a unique transition within an atom or molecule, going to have a unique lineshape?
Unique, maybe no. Remember we have also measurement accuracies in play. Few popular shapes, yes.
A lot of spectral lines (e.g. the famous sodium doublet at 589nm) are in fact multiplets and this was discovered after the equipment and measurement techniques evolved enough precision to distinguish them.
Multiplets have their intrinsic intensity ratios between the constituent lines, so yes, this can count as different shapes.
My initial reasoning leads me to say yes. Given that lifetime broadening (which gives a spectral line its natural width) concerns the energy uncertainty ΔE of the transition, and this ΔE is different for every transition in a given atom/molecule, then the lifetime broadening should be different and thus the shape as well. The other sources of broadening, like doppler or collision broadening, should apply uniformly. Is all of this correct?
I don't see flaws there.
Secondly, I'd like to ask about isotopes: different isotopes will have different, unique spectra compared to each other (even if the difference is subtle). Will the same transition in each isotope have the same lineshape? In other words, will a transition in isotope 1 have the same lineshape as the same transition in isotope 2? (By "the same", I mean that even though the frequency / energy gap is slightly different, it's still the same transition between particular orbitals).
The above consideration about the lifetime broadening still holds. Since the frequency differences are this much subtle, the lifetime broadening differences will be correspondingly subtle, but in theory will be there.
Then again, see the hyperfine structure - isotopes do have different nuclear spin, different nuclear magnetic momentum and as an effect - different hyperfine splitting.
Depending on your wavelength resolution, this may also count for different "shape" of a line or for completely different lines.
Now I see you also talk about molecules in the title of your question.
With molecules in a gas phase, everything becomes a multiplet by adding and subtracting vibrational and rotational transition energies to/from the electron transition energy.
A beautiful example e.g. here: https://opentextbc.ca/universityphysicsv3openstax/chapter/molecular-spectra/
a comment from @Landak with some good remarks:
This is a great answer, but it might also be an idea to mention the fact that Lorentzian shapes arise as the Fourier transform of an exponential damped sinusoid (i.e. natural lifetime decay) and Gaussian lineshapes arise if diffusion dominates. The situation is more complex if the experimental imperfections (or natural properties of the material studied) are considered – for an obvious but different example think of the homogeneity of the magnetic field in NMR or EPR spectroscopy where the lineshape observed can be completely changed by it.