Recommendation letter sent from non-institutional email
I use my gmail, but gmail has the capability to manage the sender addresses. You should authenticate your gmail to send from your institutional address. The recipient will then have the confirmation that you are indeed who you say you are, as gmail will have already done the authentication.

The authenticator in gmail  has the ability to either use the SMTP server of your institution to send (if your systems team permits it), where gmail is then acting as the mail client, or it can use the From headers to indicate your authenticated affiliation.

If you were doing it properly you could manage all your email through the gmail account and choose whichever outgoing account and sending method you choose. This is what I do, for the several academic institutional affiliations I possess.

So in summary: you can have it both ways. You can use gmail for official institutional correspondence and you can use the options provided in gmail to choose which of your attributions any particular email uses. It is appropriate to badge emails for official correspondence, such as letters of recommendation, with your institutional addresses. I would   suggest not using a personal email addresses for business purposes, but using the tools properly you can customise your environment in a professional manner.