First of all, to refers to the field attribute_value_ids from the field attribute_id(of the tree definition for the field webattribute_line_ids) you should use parent.attribute_value_ids but fields of attribute_value_ids are not available, meaning that you cannot do parent.attribute_value_ids.attribute_id.

For that you need to build your domain in python re-implementing search or name_search method, for that I suggest that you need to pass some values in the context of the field attribute_id in the tree. For that you need to begin to pass the contexts values from the main form. Something like this seudo-code:

<field name="webattribute_line_ids" widget="many2one_list" context="{'show_attribute': False, 'attribute_value_ids': attribute_value_ids}" nolabel="notrue">
    <field name="attribute_id" options="{'no_create': True}" context="{'attribute_value_ids': attribute_value_ids, 'special_search': True}" />
</field>

Using those values in the context you could implement your business rules for filtering those fields based on the others by re-implementing you search or name_search method.

*** Example ***

@api.model
def search(self, args, offset=0, limit=None, order=None, count=False):
    if self.env.context.get('split_name', False):
        name = False
        for item in args:
            if item[0] == 'name':
                name = item
                break
        if name:
            args.remove(name)
            name = item[2]
            domain = split_name_domain(name)
            if domain:
                args += domain
    if self.env.context.get('current_user', False):
        group_id = self.env['ir.model.data'].xmlid_to_res_id('medical_install.group_medical_doctor')
        group_user = self.env['res.groups'].search([('id', '=', group_id), ('users.id', '=', self.env.uid)])
        if group_user:
            args.extend([('partner_id', '=', self.env.user.partner_id.id)])
    return super(medical_physician, self).search(args, offset=offset, limit=limit, order=order, count=count)