Are These Ok? 我今天没锻炼。

我今天没锻炼。
I didn't work out today.

我去Starbuck了，读买了两杯冰绿茶。  I'm curious to know why you used "读".
I went to Starbucks, and bought 2 iced green teas.

我在那边会见了LJ。 
I met LJ there.

Due to my poor English, I'm not sure whether you meant to say you saw LJ by chance or by prior arrangement.

Your Chinese sentence means the latter, though it sounds too formal as "会见" is usually used for high-ranking officials. 

By the way, the attached photo I took this morning along a country road about five minutes from my house. I was heading home from Josh's house and saw the opportunity to capture the morning sun and the dew still on the leaves on digital film. I am so envious of these people. I so would love to own this property. I bet deer even come down to these neighboring field to graze during the morning! My place is in the country too but on a wooded street, so there is no gigantic field like this.

Are These Ok? 我今天没锻炼。Well this is ok.

我今天没锻炼健身。锻炼 involves every kind of  phisical exercises generally. I think work out you mentioned here is building muscle or other activities which are more likely to happen in GYM.If yes, you should use 健身 here. 
I didn't work out today.

我去Starbuck了，还读买了两杯冰绿茶。  you may already learnt that, in Mandarin, we use a '了' after a verb. in tell the other people that this action has been done or has takenplace already. 读 means read.For example, read a book-读一本书. Bought is 买了，while buy is 买. 
I went to Starbucks, and bought 2 iced green teas.

我在那边会见见到了LJ。 会见 is really a formal occasion where two or more people meet each other and have some conferences as well. You can hear a lot of political news reporters say this word, but no one around you would say it.
I met LJ there.

By the way, the attached photo I took this morning along a country road about five minutes from my house. I was heading home from Josh's house and saw the opportunity to capture the morning sun and the dew still on the leaves on digital film. I am so envious of these people. I so would love to own this property. I bet deer even come down to these neighboring field to graze during the morning! My place is in the country too but on a wooded street, so there is no gigantic field like this.