Class III stars are those in star forming regions without large non-photospheric infrared emission, suggesting recent dispersal of their protoplanetary disks. We observed 30 class III stars in the 1-3 Myr Lupus region with ALMA at ∼856μm, resulting in 4 detections that we attribute to circumstellar dust. Inferred dust masses are 0.036 − 0.093M⊕, ∼1 order of magnitude lower than any previous measurements; one disk is resolved with radius ∼80 au. Two class II sources in the field of view were also detected, and 11 other sources, consistent with sub-mm galaxy number counts. Stacking non-detections yields a marginal detection with mean dust mass ∼0.0048M⊕. We searched for gas emission from the CO J=3-2 line, and present its detection to NO Lup inferring a gas mass (4.9 ± 1.1) × 10−5 M⊕ and gas-to-dust ratio 1.0 ± 0.4. Combining our survey with class II sources shows a gap in the disk mass distribution from 0.09 − 2M⊕ for >0.7M⊙ Lupus stars, evidence of rapid dispersal of mm-sized dust from protoplanetary disks. The class III disk mass distribution is consistent with a population model of planetesimal belts that go on to replenish the debris disks seen around main sequence stars. This suggests that planetesimal belt formation does not require long-lived protoplanetary disks, i.e., planetesimals form within ∼2 Myr. While all 4 class III disks are consistent with collisional replenishment, for two the gas and/or mid-IR emission could indicate primordial circumstellar material in the final stages of protoplanetary disk dispersal. Two class III stars without sub-mm detections exhibit hot emission that could arise from ongoing planet formation processes inside ∼1 au
