Please don't put baby oil on your daughter's hair as this will make her hair very greasy and difficult to remove. I know someone who did this and she had a dreadful time. My eldest daughter caught head lice once at school and I was mortified because her hair is always immaculate but head lice are not discriminatory and will go to a clean head as well as a dirty one, anyone can catch them if they come into contact with someone who has them.
There are many options available to you ranging from chemical solutions to natural remedies. You can choose from a wide range of head lice treatments but please remember that these are insecticides and intended for occasional use only. If this is a persistent problem, then I would strongly urge you NOT to use these treatments on your daughter's hair or you will seriously ruin her hair. Straw like hair only seems to suit Worzel Gummidge.
Instead you could use conditioner to treat her hair. Apply generous amounts of conditioner to her hair to entirely coat it and then comb thoroughly with a nit comb, being careful to rinse the comb after every stroke with cold water. It is important to remove the eggs as well as the live lice to prevent reinfestation. This should be repeated every two days for a two week period (lifespan for reinfestation by means of the eggs hatching) The conditioner makes it too slippy for these ugly little blighters to cling to and they literally slide off when combed out but you must remove all the eggs. A common misconception is that the child has been reinfested time and time again but if you do not ensure that all the eggs are removed then the cycle continues and around two weeks later, your child will have head lice again.
For a wash in shampoo treatment you could use clean & clear head lice shampoo which is intended for frequent use for a habitual problem and it's effects are less severe on the individual's hair. Hope this helps x