We present ALMA observations of 101 protoplanetary disks within the star-forming region Lynds 1641 in the Orion Molecular Cloud A. Our observations include 1.33 mm continuum emission and spectral windows covering the J=2-1 transition of ^12^CO, ^13^CO, and C^18^O. We detect 89 protoplanetary disks in the dust continuum at the 4{sigma} level (~88% detection rate) and 31 in ^12^CO, 13 in ^13^CO, and 4 in C^18^O. Our sample contains 23 transitional disks, 20 of which are detected in the continuum. We target infrared-bright Class II objects, which biases our sample toward massive disks. We determine dust masses or upper limits for all sources in our sample and compare our sample to protostars in this region. We find a decrease in dust mass with evolutionary state. We also compare this sample to other regions surveyed in the (sub)millimeter and find that Lynds 1641 has a relatively massive dust disk population compared to regions of similar and older ages, with a median dust mass of 11.1_-4.6_^+32.9^M_{Earth}_ and 27% with dust masses equal to or greater than the minimum solar nebula dust mass value of ~30M_{Earth}_. We analyze the disk mass-accretion rate relationship in this sample and find that the viscous disk lifetimes are similar to the age of the region, though with a large spread. One object, [MGM2012] 512, shows a large-scale (>5000au) structure in both the dust continuum and the three gas lines. We discuss potential origins for this emission, including an accretion streamer with large dust grains.