The Lori-Bakhtiari fat-tailed sheep is one of the most important heavyweight native breeds of Iran. The breed is robust and well adapted to semi-arid regions and an important resource for smallholder farms. An established nucleus-based breeding scheme is used to improve their production traits but there is an indication of inbreeding depression and loss of genetic diversity due to selection. Here, we estimated the inbreeding levels and the distribution of runs of homozygosity (ROH) islands in 122 multigenerational female Lori-Bakhtiari from different half-sib families selected from a breeding station that were genotyped on the 50k array. A total of 2404 ROH islands were identified. On average, there were 19.70 ± 1.4 ROH per individual ranging between 6 and 41. The mean length of the ROH was 4.1 ± 0.14 Mb. There were 1999 short ROH of length 1–6 Mb and another 300 in the 6–12 Mb range. Additionally long ROH indicative of inbreeding were found in the ranges of 12–24 Mb (95) and 24–48 Mb (10). The average inbreeding coefficient (FROH) was 0.031 ± 0.003 with estimates varying from 0.006 to 0.083. Across generations, FROH increased from 0.019 ± 0.012 to 0.036 ± 0.007. Signatures of selection were identified on chromosomes 2, 6, and 10, encompassing 55 genes and 23 QTL associated with production traits. Inbreeding coefficients are currently within acceptable levels but across generations, inbreeding is increasing due to selection. The breeding program needs to actively monitor future inbreeding rates and ensure that the breed maintains or improves on its current levels of environmental adaptation.