The strong showing in home building here continued in June when 19 building permits were issued for single-family homes, almost double the total for June 1982.

After a small tax decrease the past year, Lawrence property-owners were facing a 10-mill tax hike for 1984 if preliminary figures became final. Tax levies being projected by the city, county and school district added up to a 130.45-mill levy. The city was considering a 1.81-mill hike, the county a 4.56 boost and the school board a 3.70-mill increase.