Understanding "英語のレッスンしないとな"


The sentence

> 英語のレッスンしないとな。

apparently translates to

> I need English lessons.

However it seems to me this sentence means something like

> Don't do English lessons, ???

so I'm pretty terribly confused.

**Other Questions:**

  1. What is the とな at the end signify? My best guess it something like "it's been said, eh?" (with と being used as the quotation particle).
  2. If I'm right on (1), does this sentence mean something like "It's been said I don't do English lessons, eh?"




まずは少し文法を勉強しないとな。  
Which is to say: to understand this construction, you "need to" learn how to
express “need to” in Japanese. I recommend you read the following
comprehensive _Guide To Japanese_ article from start to finish: [_Expressing
“must” or “have to”_](http://guidetojapanese.org/learn/grammar/must).

* * *

As you'll see, there are many forms of what is essentially the same
construction. The first half of that article covers the unabbreviated forms,
which includes the と-form with 2 examples:

[code]

    毎日学校に行かないとだめです。
    Must go to school everyday.
    宿題をしないといけない
    Have to do homework.
    
[/code]

The second part of that article mentions their abbreviated forms, which are
actually a lot more commonly used than their verbose counterparts—in
spoken/casual language at least. Here you'll find the abbreviated と-form too:

> The 「と」 conditional is also used by itself to imply 「だめ／いけない／ならない」.
[code]

    学校に行かないと。
    Gotta go to school.
    
[/code]

