There is proof that Johannes Lorentz (b.1666) (which some refer to John, but according to records it is Johannes) arrived to America at the age of 43 with his wife Anna Margaretha Heiliger (b. 1671, age 39) with their children on May 23, 1709 on the ship "Medford".
It looks like you have some names mixed up. I have noticed this lines likes to reuse names (for example - Johannes and Anna have 3 daughters names Anna). To make everything more complicated in most records their kids last name name changed to Lowrance from Lorentz.It is also common for brothers and sisters to marry other brother/sisters.
As far as their kids: There is a Anna Barbara Lowrance born 9/3/1700, she could have married a John Eveland.
I do know that Alexander Lowrance (b. 1709) married a Mary Eveland (do not know anything for her) in 1730.
Anna and Alex have a brother named John and well.So it is possible that Anna was married to John Eveland since he would have a brother in law named John.
As far as a Johann Jacob Beshearer.. I think there is some mix up.I do know that one of Johannes kids name is Johan Jacob Lowrance but I have it down that he was born 1707 and died in 1709.
Johannes and Anna did have a son names John Lowrance as well.According to his last known will done 3 days before his death in 1781, his wife is stated as "Anne Lorence". He may have been married before her.
Johannes Lorentz parents are Hans Heinrich Lorentz and Mary Townly.
Also, just so you know.Alexander and Mary (Evelyn) Lorentz, son Peter Lowrance (b. 1736) had two wifes.With his first wife (Anne Baker) the kids adapt the last name spelt Lieurance while his kids with his second wife (Elizabeth Bridges) took the Lowrance spelling.
If you have any questions, feel free to contact me.If I am leaving anyhting out let me know.