We've set up a workflow rule to update a field using time based action and set up another workflow rule to convert the lead based on that field updating. Seemed , field updating working fine but it can't convert the lead. Is it not possible to automate the lead conversion in such way?

Let me explain little bit- we are getting lead from third party tool using Zapier. When we get qualified lead we want to get it converted to contacts and potential automatically. We know, converting works only on field update or edit trigger action. so we have created a time based action to update a field based on record creation. It updates the field after specified time but doesn't trigger the other rule that is defined for conversion. 

How can we automate this conversion if the above process doesn't support?

Thanks,

Wasiur