Hi Rosalie,
Thank you for your message. I did a search for Eliza on the Famine Orphan Girl Database-is this where you found your information?
http://www.irishfaminememorial.org/orphans/database/?surName=Walsh&firstName=&age=0&nativePlace=&parents=&religion=0&ship=20
In order to confirm her parents you will have to find her birth records. As Castlelost is listed as her native place this is probably the best place to start. You will need to look at church records as civil registration did not begin until 1864. Most Catholic records are held locally so you may need to write to the local parish priest for possible assistance. One website that you may find useful is the Irish Times where they give an overview of what records are available in specific parishes. It also shows you where copies of the records are available. Castlelost belongs to the Catholic parish of Rochfortbridge. Records there begin as early as 1821 so hopefully you will be able to find something:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&churchid=959&CityCounty=Westmeath&CityCounty=Westmeath&parish=Rochfortbridge
As you can see from the above link Dun na Si Heritage Centre in Westmeath have copies available. If you would like to contact them here is their email, however a fee may apply: dunnasimoate@eircom.net
With regards to records of the workhouse, you should contact Westmeath County Library HQ. Here is a link to the webpage:
http://www.westmeathcoco.ie/en/ourservices/tourismartsrecreation/libraryservice/localstudies/archives/
Some other websites that you may find useful are:
The National Archives of Ireland http://www.nationalarchives.ie/genealogy1/genealogy-records/introduction/
The National Library of Ireland http://www.nli.ie/en/family-history-introduction.aspx
Genealogy links: http://www.genealogylinks.net/uk/ireland/westmeath/index.html
The Workhouse: http://www.genealogylinks.net/uk/ireland/westmeath/index.html
From Ireland: http://www.from-ireland.net/
I hope this is helpful.
All the best,
Genealogy Support