How can I call lanes with parameters from within my lane?

You should do it in this way:

lane :my_lane do
  other_lane(
    parameter1: '1', 
    parameter2: '2'
  )
end

Hope this helps!

So other lane should be

lane :other_lane do |values|
   parameter1  = values[:parameter1]
   parameter2  = values[:parameter2]
   puts parameter1
   puts parameter2
end