Under EASA rules you may get a Class 2 medical - which is valid for a PPL - if you fail the various tests but may/will be awarded a VCL limitation that means Valid by Day Only. Same for LAPL medical - but you cannot hold instrument or instructing qualifications on a LAPL(A), and I'm not sure but a LAPL probably restricts you to SEP under 2000 kg.
The CAA do have an alternative to the lantern test.
(c) Those failing the Ishihara test should be examined by:
(1) Anomaloscopy (Nagel or equivalent). This test is considered passed if the colour match shows normal trichromacy, i.e. a matching midpoint of 38-42 scale units and the matching range is 4 scale units or less; or by
(2) Colour Assessment and Diagnosis (CAD) Test. This is considered passed if the threshold is less than 6 SU for deutan deficiency, or less than 12 SU for protan deficiency. A threshold greater than 2SU for tritan deficiency indicates an acquired cause which should be investigated.
Details of EASA rules in the Annex to ED Decision 2011/015/R - the AMCs and GM to Part Med.