I don't know why so many people always suggest to hire a lawyer for things like this. You can do most legal things in DR without a lawyer, even if your Spanish is limited. I don't remember when I needed to use a lawyer last time, 10 years ago maybe? or 15 years ago?
If you lost any document issued in DR, you have to go to the office where it was issued and ask what exactly is needed to reissue it. Keep in mind that what's needed today maybe not exactly what was needed a year or two ago, or the fees have changed, etc. So, if you live in US now, you better just call that office responsible for your type of document (Registro de Titulos in your case) and ask them what exactly is needed now for that and ask for all details (how long, how much, the list of documents required, etc). In general, it will be what Winkeladvocat described in the post above, so just call them and ask is it still like that or something has changed. Then you will know how to plan your trip to DR for that and what to expect.