To keep a living thing implies a kind of ownership, or oversight, like with farm animals or pets:
When he was young their family kept chickens, so he was used to having fresh eggs every morning.
"Do you like dogs?" he asked. "No," she replied, "but I do keep an unruly tomcat named Sam".
You'd only use it with people in very limited contexts. For example, if you say you keep a mistress, it implies that you pay for all her necessary living expenses. Ancient Romans kept slaves, meaning they were treated as property.
In a different context, you could say that a business keeps a few attorneys (or any other job title) on staff, as if they were tools, paid to perform a particular service.
The high-class hotel always kept a doctor on call in case one of its guests had any urgent (and private) medical needs.
The tone of these varies. "Keeping slaves" dehumanizes the slaves to the status of owned objects, and "keeping a mistress" implies a subservient (or at least dependent) role, but "keeping an doctor" is not usually negative.
Lastly, "the Lord keep you" is short for a longer expression, something like
May the Lord keep you from harm
The Lord bless you and keep you from need
This is a different definition; here to keep from means "to prevent".