The jobless rate in the state climbed slightly last month, while in Lake County it remained unchanged. The Employment Development Department said the September unemployment rate in Lake County was 5.6%, the same rate as in August. The jobless rate was 4.3% at this time a year ago. Most of the county’s job sectors showed declines, except for private service providing, which grew by 1.1%, and private education and health services, which grew by 4.5%.