Still, Tcl's anonymous functions aren't quite what many people consider to be lambdas:
% set inc {x {expr $x + 1}}
% apply $inc 1
2
% apply $inc 1
2
% $inc 1
invalid command name "x {expr $x + 1}"
% inc 1
1
I'm not saying it's inadequate, just that the anonymous functions don't quite work how you expect lambdas to work.
One thing to note though, your final [inc 1] has nothing to do w/ $inc. In the interactive REPL (which I'm assuming you used), Tcl will (by default) essentially autocomplete commands if it can, and [inc] completed to [incr], which is "increment". [incr] adds (by default) 1 to the named variable and returns its result. In this case, the variable name happens to be "1", later accessible via "$1", or [set 1], for example.
[edit: I erroneously initially described the "1" in [incr 1] as the integer constant 1; @groovy2shoes reply below reflects my original error. This does go to show another neat feature of Tcl: no keywords.]
I find Tcl's command model interesting because it leads to a very tiny semantics. A few years ago I spent a lot of time thinking about how it could be extended to have lambdas, and I couldn't come up with a way that wouldn't break the command model in some way or another. They aren't something Tcl needs to have, I just thought it'd be convenient. (Tcl's evaluation model allows you to simulate higher-order procs, which, along with `apply`, covers many use cases of lambda).
$ tclsh
% set a set
set
% puts $a
set
% $a b 9
9
% set b
9
% set set set
set
% $set set
set
% rename set foo
% foo set
set
% foo a
set
% foo a 9
9
% puts $a
9
%
[edit: formatting]