We have computed the thermally averaged total, elastic rate coefficient for the collision of a room-temperature helium atom with an ultracold lithium atom. This rate coefficient has been computed as part of the characterization of a cold-atom vacuum sensor based on laser-cooled Li-6 or Li-7 atoms that will operate in the ultrahigh-vacuum (p < 10(-6) Pa) and extreme-high-vacuum (p < 10(-10) Pa) regimes. The analysis involves computing the X (2) Sigma(+) HeLi Born-Oppenheimer potential followed by the numerical solution of the relevant radial Schrodinger equation. The potential is computed using a single-reference-coupled-cluster electronic-structure method with basis sets of different completeness in order to characterize our uncertainty budget. We predict that the rate coefficient for a 300 K helium gas and a 1 mu K Li gas is 1.467(13) x 10(-9) cm(3)/s for He-4 + Li-6 and 1.471(13) x 10(-9) cm(3)/s for He-4 + Li-7, where the numbers in parentheses are the one-standard-deviation uncertainties in the last two significant digits. We quantify the temperature dependence as well. Finally, we evaluate the s-wave scattering length and binding of the single van der Waals bound state of HeLi. We predict that this weakly bound level has a binding energy of -0.0064(43) x hc cm(-1) and -0.0122(67) x hc cm(-1) for He-4 + Li-6 and He-4 + Li-7, respectively. The calculated binding energy of He-4 + Li-7 is consistent with the sole experimental determination.