Ultralight bosons with self-interactions, such as axion-like particles, can form astrophysical Bose–Einstein condensates around stars or compact objects, often referred to as gravitational atoms. In this work, we adopt a recently proposed dynamical formation mechanism for these halos and estimate their impact on extreme- and intermediate-mass-ratio inspirals when present around the primary black hole. We show that, for signal-to-noise ratios $\lesssim 100$, LISA can distinguish gravitational waveforms from binaries embedded in such halo overdensities. Our analysis indicates that LISA can probe boson masses $m_{dm}\sim {10}^{-17}$–${10}^{-15}eV$ and decay constants $f_a\sim 3\times {10}^{10}$–$6\times {10}^{12}GeV$ using binaries with total masses $M\sim {10}^4$–${10}^5{M}_{\odot }$, . Allowing for higher background densities and different extreme-mass-ratio configurations further extends the accessible parameter space. Moreover, we find that for a binary configuration with $M\sim {10}^4{M}_{\odot }$, $\rho_{\rm dm} = 10^4\,\mathrm{GeV/cm^3}$, and signal to noise ratio $\mathrm{\text{SNR}}\sim 20$, a particle mass of $m_{dm}=3.2\cdot {10}^{-15}$ eV and decay constant of $f_a=1.6\cdot {10}^{11}$ GeV maximize the dephasing due to dynamical friction, enabling the recovery of the particle parameters at the percent level. These results demonstrate that LISA can place constraints on axion-like particle masses and self-interactions without requiring additional couplings to Standard Model fields.