Dear Katerina Tsiko thank you for sharing this very interesting technical question with the RG community. Although we work in the field of lanthanide chemistry for ca. 40 years, I never came across a simple spot test for lanthanides. When searching for answers to your question, I came across a spot test which has been developed particularly for the detection of cerium +3 (see attached). It was mentioned in the book "Chemistry of Lanthanides and Actinides" published by G. Singh.
In addition, please have a look at the followig potentially useful article which might help you in your analysis:
Analytical method for detecting and estimating of lanthanide ions paired with transitional elements
Article Analytical method for detecting and estimating of lanthanide...
This paper has been posted by the authors as public full text on RG, so that you can freely download it as pdf file.
Particularly concerning the analysis of lanthanide-containing preciptates, please also check the following relevant literature reference:
Trace analysis of lanthanides by laser excitation of precipitates
Article Trace Analysis of Lanthanides by Laser Excitation of Precipitates
This paper is a bit older, and the public full text is unavailable on RG. Please check if you can access the full text through your institution.
I hope this helps a bit. Good luck with your research and best wishes, Frank Edelmann