Support for chunked encoding is independent from the SSL backend (i.e. Crypt::SSLeay or IO::Socket::SSL). And as far as I know LWP supports chunked encoding both for requests and for responses as required by HTTP/1.1.
Could you please show a test program (with a URL you have problems with) so that other can reproduce your problem? And please note the versions of LWP::UserAgent and IO::Socket::SSL you are using.