It’s not quite clear whether you have an access to a command line to generate your certificate or not (since you might be using something specific for that hosting company you mentioned).
If you can use a command line, then it depends on what kind of Let’s Encrypt client is installed. For example, the official one has an option for manual mode. I do believe that alternative clients would have something similar, though I can only be sure about mine (Crypt::LE), since I haven’t tested those.
If you have your Let’s Encrypt account key for example in the account.key file and your subdomain is “some.domain.com”, then running it like this would do the job:
le.pl --key account.key --csr some-domain.csr --csr-key some-domain.key --crt some-domain.crt --domains “some.domain.com” --generate-missing --live
You would be asked to put a specific text into a file with a specific name under .well-known/acme-challenge/ in the webroot directory of that server which your subdomain is pointing to and press Enter. After that you can find the key and certificate you’ve asked for in some-domain.key and some-domain.crt.