Author: Alan, 5B4AHJ

RSGB DX News Sheet #1387, dated 1989-10-18, reports:

"The three Baltic states of Estonia, Latvia and Lithuania were independent states before WWII, but were incorporated into the USSR during the war. As independent states, they were allocated special amateur prefixes UR, UQ and UP. At the beginning of October, the Amateur Radio Society of Lithuania received approval from the authorities in Moscow to replace the UP prefix with LY. Over 100 Lithuanian stations are now using the LY prefix, and the number is increasing daily."

However, the change appears to have taken place in October, 1988, not October, 1989. See for example, the QSL of LY2WW for a QSO on 1988-10-29.

RSGB DX News Sheet #1387 also reports:

 "Amateurs in Estonia are soon expected to start using callsigns in the series ES1-ES0. The country will be divided into 10 call areas similar to those which existed before WWII."

RSGB DX News Sheet #1398, dated 1990-01-10, reports:
"The new ES callsigns have appeared from Estonia. The prefix number indicates the province  as follows (tnx LNDX):
ES1 Tallin and northern islands
ES2 Harju  Rajon
ES3 Haapsalu, Rapla and Paide
ES4 Kohtla-Jarve, Sillamae, Rakvere and Narva
ES5 Tartu, Jogeva and Polca
ES6 Valga and Voru
ES7 Viljandi
ES8 Parnu
ES9 special events."

Regarding Latvia, I have not found any documentation regarding the change to the YL prefix.
However, inspecting the Club Log QSL database and various QSLs, I believe that the change happened in October, 1988. 

Based on the above, and feedback from Club Log users, Club Log maps the ES, YL and LY prefixes for these entities as follows:
Old prefix New prefix DXCC entity Start date of new prefix used by Club Log
UR ES Estonia 1989-12-31 (=1990-01-01 local time)
UQ YL Latvia 1988-09-30
UP LY Lithuania 1988-09-30

UR2RMC became ES5MC
UP1BZZ became LY2ZZ

There seems to have been a long overlap between the introduction of the new prefixes, and the phasing out of the old callsigns. For example, UQ2GMK was still QRV in July, 1990, and UP3BK was still QRV in May, 1989.

RSGB DX News Sheets