Can I use an internet fax service if my computer is on an office network (LAN)?

Usually, yes. Internet fax services normally work through email - faxes received for you are forwarded to you as attachments by email, faxes you send are accepted from you by email.

For fax transmission, make sure that your network administrator hasn't set the limit for outbound attachment sizes too low for you to send your documents. For fax reception, make sure that your network administrator allows inbound attachments, and doesn't mark TIF attachments as viruses or spam.