An Séimhiú agus an tUrú
JavaScript (ES6),  98  97 bytes
Returns an array [lenited, eclipsed].
s=&gt;[(x=[...'2n1111gbnd1m1','bh',2][parseInt(c=s[0],30)*17%22])&gt;'1'?c+'h'+s.slice(1):s,x&gt;{}?x+s:s]

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How?
We define the following lookup table:
A = [ ...'2n1111gbnd1m1', 'bh', 2 ]

//     0    1    2    3    4    5    6    7    8    9    10   11   12   13  14
A = [ '2', 'n', '1', '1', '1', '1', 'g', 'b', 'n', 'd', '1', 'm', '1', 'bh', 2 ]

where:

a single character (or the string &quot;bh&quot;) is used for eclipsis; all letters that trigger eclipsis also trigger lenition
\$1\$ means that there's no eclipsis and no lenition
\$2\$ means that there's no eclipsis but there is lenition

The first letter of the input word is converted from Base30 to decimal, multiplied by \$17\$ and then reduced with a modulo \$22\$. The result is used to pick the correct value from \$A\$.
Any result above \$14\$ yields undefined, and so does any letter in the range u-z or any fada vowel. An undefined value is interpreted the same way as \$1\$ (no eclipsis, no lenition).
  1st letter | from Base30 | * 17 | mod 22 | A[n]
-------------+-------------+------+--------+-----------
      a      |      10     |  170 |   16   | undefined
      b      |      11     |  187 |   11   | 'm'
      c      |      12     |  204 |    6   | 'g'
      d      |      13     |  221 |    1   | 'n'
      e      |      14     |  238 |   18   | undefined
      f      |      15     |  255 |   13   | 'bh'
      g      |      16     |  272 |    8   | 'n'
      h      |      17     |  289 |    3   | '1'
      i      |      18     |  306 |   20   | undefined
      j      |      19     |  323 |   15   | undefined
      k      |      20     |  340 |   10   | '1'
      l      |      21     |  357 |    5   | '1'
      m      |      22     |  374 |    0   | '2'
      n      |      23     |  391 |   17   | undefined
      o      |      24     |  408 |   12   | '1'
      p      |      25     |  425 |    7   | 'b'
      q      |      26     |  442 |    2   | '1'
      r      |      27     |  459 |   19   | undefined
      s      |      28     |  476 |   14   | 2
      t      |      29     |  493 |    9   | 'd'
 u-z or fada |     NaN     |  NaN |  NaN   | undefined