When I write a lambda with [=], does it mean that all my local variables will be copied into members of the created struct or can I assume that only those will that
No! (thankfully)
You can instrument your code to check whether your compiler actually does it (or not). For example gcc 4.8.0 appears to be compliant.
As to what the Standard actually mandates (working backward):
§5.1.2/14 An entity is captured by copy if it is implicitly captured and the capture-default is
=or if it is explicitly captured with a capture that does not include an&. For each entity captured by copy, an unnamed nonstatic data member is declared in the closure type.$5.1.2/11 If a lambda-expression has an associated capture-default and its compound-statement odr-uses (3.2)
thisor a variable with automatic storage duration and the odr-used entity is not explicitly captured, then the odr-used entity is said to be implicitly captured; such entities shall be declared within the reaching scope of the lambda expression.§5.1.2/9 A lambda-expression whose smallest enclosing scope is a block scope (3.3.3) is a local lambda expression; any other lambda-expression shall not have a capture-list in its lambda-introducer. The reaching scope of a local lambda expression is the set of enclosing scopes up to and including the innermost enclosing function and its parameters. [ Note: This reaching scope includes any intervening lambda-expressions. —end note ]