We have an Azure logic app that fires every 60 seconds. It fetches a URL. Typically this would only take < 1s, but sometimes if there's a lot of work to do on the other end it can be higher.
Will the Azure logic app service wait to fire again if the previous request is still pending or will it just fire again regardless?
No it will not wait for the previous job to complete, it will fire again.
If you want it to not run if a previous job is not running you would need to add something to your logic app to check for that first.